2000 character limit reached
A Preconditioned Interior Point Method for Support Vector Machines Using an ANOVA-Decomposition and NFFT-Based Matrix-Vector Products (2312.00538v1)
Published 1 Dec 2023 in math.NA, cs.LG, cs.NA, and math.OC
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)
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.