2000 character limit reached
A Preconditioned Interior Point Method for Support Vector Machines Using an ANOVA-Decomposition and NFFT-Based Matrix-Vector Products
Published 1 Dec 2023 in math.NA, cs.LG, cs.NA, and math.OC | (2312.00538v1)
Abstract: In this paper we consider the numerical solution to the soft-margin support vector machine optimization problem. This problem is typically solved using the SMO algorithm, given the high computational complexity of traditional optimization algorithms when dealing with large-scale kernel matrices. In this work, we propose employing an NFFT-accelerated matrix-vector product using an ANOVA decomposition for the feature space that is used within an interior point method for the overall optimization problem. As this method requires the solution of a linear system of saddle point form we suggest a preconditioning approach that is based on low-rank approximations of the kernel matrix together with a Krylov subspace solver. We compare the accuracy of the ANOVA-based kernel with the default LIBSVM implementation. We investigate the performance of the different preconditioners as well as the accuracy of the ANOVA kernel on several large-scale datasets.
- Platt, J.: Sequential minimal optimization: A fast algorithm for training support vector machines. Technical Report MSR-TR-98-14 (1998) Osuna et al. [1997] Osuna, E., Freund, R., Girosi, F.: An improved training algorithm for support vector machines. In: Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop, pp. 276–285 (1997). IEEE Fine and Scheinberg [2001] Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research 2(Dec), 243–264 (2001) Harbrecht et al. [2012] Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Osuna, E., Freund, R., Girosi, F.: An improved training algorithm for support vector machines. In: Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop, pp. 276–285 (1997). IEEE Fine and Scheinberg [2001] Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research 2(Dec), 243–264 (2001) Harbrecht et al. [2012] Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research 2(Dec), 243–264 (2001) Harbrecht et al. [2012] Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Osuna, E., Freund, R., Girosi, F.: An improved training algorithm for support vector machines. In: Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop, pp. 276–285 (1997). IEEE Fine and Scheinberg [2001] Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research 2(Dec), 243–264 (2001) Harbrecht et al. [2012] Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research 2(Dec), 243–264 (2001) Harbrecht et al. [2012] Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research 2(Dec), 243–264 (2001) Harbrecht et al. [2012] Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Harbrecht, H., Peters, M., Schneider, R.: On the low-rank approximation by the pivoted Cholesky decomposition. Applied Numerical Mathematics 62(4), 428–440 (2012) Yang et al. [2003] Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Yang, C., Duraiswami, R., Gumerov, N.A., Davis, L.: Improved fast Gauss transform and efficient kernel density estimation. In: Proceedings of the IEEE International Conference on Computer Vision (2003). IEEE Computer Society Alfke et al. [2018] Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Alfke, D., Potts, D., Stoll, M., Volkmer, T.: NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks. Frontiers in Applied Mathematics and Statistics 4 Art. 61 (2018) Nestler et al. [2022] Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Nestler, F., Stoll, M., Wagner, T.: Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication. Foundations of Data Science 4(3), 423–440 (2022) Stoll [2020] Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Stoll, M.: A literature survey of matrix methods for data science. GAMM-Mitteilungen 43 e202000013(3) (2020) Forsgren et al. [2002] Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Review 44(4), 525–597 (2002) Gondzio [2012] Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Gondzio, J.: Interior point methods 25 years later. European Journal of Operational Research 218(3), 587–601 (2012) Nesterov and Nemirovskii [1994] Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Nesterov, Y., Nemirovskii, A.: Interior Point Polynomial Algorithms in Convex Programming: Theory and Applications. SIAM, Philadelphia, PA (1994) Potra and Wright [2000] Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Potra, F.A., Wright, S.J.: Interior-point methods. Journal of Computational and Applied Mathematics 124(1–2), 281–302 (2000) Wright [1997] Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA (1997) Avron et al. [2017] Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Avron, H., Clarkson, K.L., Woodruff, D.P.: Faster kernel ridge regression using sketching and preconditioning. SIAM Journal on Matrix Analysis and Applications 38(4), 1116–1138 (2017) Cai et al. [2022] Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Cai, D., Nagy, J., Xi, Y.: Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets. SIAM Journal on Matrix Analysis and Applications 43(2), 1003–1028 (2022) Cutajar et al. [2016] Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Cutajar, K., Osborne, M.A., Cunningham, J.P., Filippone, M.: Preconditioning kernel matrices. In: International Conference on Machine Learning, pp. 2529–2538 (2016) Martinsson and Voronin [2016] Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Martinsson, P.-G., Voronin, S.: A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices. SIAM Journal on Scientific Computing 38(5), 485–507 (2016) Cortes and Vapnik [1995] Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20(3), 273–297 (1995) Benzi et al. [2005] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005) Elman et al. [2014] Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Elman, H.C., Silvester, D.J., Wathen, A.J.: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, 2nd edn. Oxford University Press, Oxford, UK (2014) Paige and Saunders [1975] Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis 12(4), 617–629 (1975) Saad and Schultz [1986] Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7(3), 856–869 (1986) Von Luxburg [2007] Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007) Potts and Steidl [2003] Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFT. SIAM Journal on Scientific Computing 24(6), 2013–2037 (2003) Morariu et al. [2008] Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Morariu, V.I., Srinivasan, B.V., Raykar, V.C., Duraiswami, R., Davis, L.S.: Automatic online tuning for fast Gaussian summation. Advances in Neural Information Processing Systems 21 (2008) March et al. [2015] March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- March, W.B., Xiao, B., Biros, G.: ASKIT: Approximate skeletonization kernel-independent treecode in high dimensions. SIAM Journal on Scientific Computing 37(2), 1089–1110 (2015) Golub and Van Loan [1996] Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996) Chen et al. [2023] Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Chen, Y., Epperly, E.N., Tropp, J.A., Webber, R.J.: Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations. arXiv preprint arXiv:2207.06503 (2023) Drineas et al. [2005] Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Drineas, P., Mahoney, M.W., Cristianini, N.: On the Nyström method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research 6(72), 2153–2175 (2005) Martinsson [2019] Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Martinsson, P.-G.: Randomized methods for matrix computations. In: Mahoney, M.W., Duchi, J.C., Gilbert, A.C. (eds.) The Mathematics of Data, pp. 187–229. American Mathematical Society & SIAM, Providence, RI (2019) Rahimi and Recht [2007] Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Rahimi, A., Recht, B.: Random features for large-scale kernel machines. Advances in Neural Information Processing Systems 20 (2007) Plonka et al. [2018] Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Plonka, G., Potts, D., Steidl, G., Tasche, M.: Numerical Fourier Analysis. Birkhäuser Cham, Springer Nature Switzerland AG (2018) Rahimi and Recht [2008] Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. Advances in Neural Information Processing Systems 21 (2008) Elgammal et al. [2003] Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient kernel density estimation using the fast Gauss transform with applications to color modeling and tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1499–1504 (2003) Halko et al. [2011] Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM Review 53(2), 217–288 (2011) Saad [2003] Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA (2003) Murphy et al. [2000] Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Murphy, M.F., Golub, G.H., Wathen, A.J.: A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 21(6), 1969–1972 (2000) Woodbury [1950] Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Woodbury, M.A.: Inverting modified matrices. Technical Report, Statistical Research Group, Princeton University, Princeton, NJ (1950) Whiteson [2014a] Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Whiteson, D.: HIGGS. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C5V312 (2014) Whiteson [2014b] Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Whiteson, D.: SUSY. UC Irvine Machine Learning Repository. DOI: https://doi.org/10.24432/C54606 (2014) Uzilov et al. [2006] Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinformatics 7 Art. 173 (2006) Chang and Lin [2011] Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2 Art. 27(3) (2011) Glowinski and Marroco [1975] Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Analyse Numérique 9, 41–76 (1975) Gabay and Mercier [1976] Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976) Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
- Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2(1), 17–40 (1976)
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.