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Survey of a Class of Iterative Row-Action Methods: The Kaczmarz Method (2401.02842v2)
Published 5 Jan 2024 in math.NA and cs.NA
Abstract: The Kaczmarz algorithm is an iterative method that solves linear systems of equations. It stands out among iterative algorithms when dealing with large systems for two reasons. First, at each iteration, the Kaczmarz algorithm uses a single equation, resulting in minimal computational work per iteration. Second, solving the entire system may only require the use of a small subset of the equations. These characteristics have attracted significant attention to the Kaczmarz algorithm. Researchers have observed that randomly choosing equations can improve the convergence rate of the algorithm. This insight led to the development of the Randomized Kaczmarz algorithm and, subsequently, several other variations emerged. In this paper, we extensively analyze the native Kaczmarz algorithm and many of its variations using large-scale dense random systems as benchmarks. Through our investigation, we have verified that, for consistent systems, various row sampling schemes can outperform both the original and Randomized Kaczmarz method. Specifically, sampling without replacement and using quasirandom numbers are the fastest techniques. However, for inconsistent systems, the Conjugate Gradient method for Least-Squares problems overcomes all variations of the Kaczmarz method for these types of systems.
- Bicer, T., Gürsoy, D., Andrade, V.D., Kettimuthu, R., Scullin, W., Carlo, F.D., Foster, I.T.: Trace: a high-throughput tomographic reconstruction engine for large-scale datasets. Advanced structural and chemical imaging 3, 1–10 (2017) Senning [2007] Senning, J.R.: Computing and estimating the rate of convergence. Gordon College, Wenham (2007) Ma et al. [2015] Ma, A., Needell, D., Ramdas, A.: Convergence properties of the randomized extended Gauss–Seidel and Kaczmarz methods. SIAM Journal on Matrix Analysis and Applications 36(4), 1590–1604 (2015) Strohmer and Vershynin [2007] Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Senning, J.R.: Computing and estimating the rate of convergence. Gordon College, Wenham (2007) Ma et al. [2015] Ma, A., Needell, D., Ramdas, A.: Convergence properties of the randomized extended Gauss–Seidel and Kaczmarz methods. SIAM Journal on Matrix Analysis and Applications 36(4), 1590–1604 (2015) Strohmer and Vershynin [2007] Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Ma, A., Needell, D., Ramdas, A.: Convergence properties of the randomized extended Gauss–Seidel and Kaczmarz methods. SIAM Journal on Matrix Analysis and Applications 36(4), 1590–1604 (2015) Strohmer and Vershynin [2007] Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. 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Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
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[2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Ma, A., Needell, D., Ramdas, A.: Convergence properties of the randomized extended Gauss–Seidel and Kaczmarz methods. SIAM Journal on Matrix Analysis and Applications 36(4), 1590–1604 (2015) Strohmer and Vershynin [2007] Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Ma, A., Needell, D., Ramdas, A.: Convergence properties of the randomized extended Gauss–Seidel and Kaczmarz methods. SIAM Journal on Matrix Analysis and Applications 36(4), 1590–1604 (2015) Strohmer and Vershynin [2007] Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Strohmer, T., Vershynin, R.: A Randomized Kaczmarz Algorithm with Exponential Convergence. Journal of Fourier Analysis and Applications 15, 262–278 (2007) Needell [2010] Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
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SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. 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[1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D.: Randomized Kaczmarz solver for noisy linear systems. BIT Numerical Mathematics 50(2), 395–403 (2010) Schmidt [2015] Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
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[1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Schmidt, M.: Notes on Randomized Kaczmarz. Randomized Algorithms (2015) Sloan and Joe [1994] Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press (1994) Halton [1960] Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
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In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, 84–90 (1960) Sobol [1976] Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Sobol, I.M.: Uniformly distributed sequences with an additional uniform property. USSR Computational Mathematics and Mathematical Physics 16(5), 236–242 (1976) Elfving [1980] Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numerische Mathematik 35, 1–12 (1980) Needell and Tropp [2014] Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear Algebra and its Applications 441, 199–221 (2014) Wang et al. [2016] Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
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[2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Wang, L., Wu, W., Xu, Z., Xiao, J., Yang, Y.: Blasx: A high performance level-3 blas library for heterogeneous multi-gpu computing. In: Proceedings of the 2016 International Conference on Supercomputing, pp. 1–11 (2016) Leventhal and Lewis [2010] Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Leventhal, D., Lewis, A.S.: Randomized methods for linear constraints: convergence rates and conditioning. Mathematics of Operations Research 35(3), 641–654 (2010) Needell et al. [2015] Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra and its Applications 484, 322–343 (2015) Zouzias and Freris [2013] Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM Journal on Matrix Analysis and Applications 34(2), 773–793 (2013) Rokhlin and Tygert [2009] Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Rokhlin, V., Tygert, M.: A fast randomized algorithm for orthogonal projection. arXiv preprint arXiv:0912.1135 (2009) Bai and Wu [2018] Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Bai, Z.-Z., Wu, W.-T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM Journal on Scientific Computing 40(1), 592–606 (2018) Yaniv et al. [2021] Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Yaniv, Y., Moorman, J.D., Swartworth, W., Tu, T., Landis, D., Needell, D.: Selectable Set Randomized Kaczmarz. arXiv preprint arXiv:2110.04703 (2021) Moorman et al. [2021] Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Moorman, J.D., Tu, T.K., Molitor, D., Needell, D.: Randomized Kaczmarz with averaging. BIT Numerical Mathematics 61(1), 337–359 (2021) Gordon and Gordon [2005] Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Gordon, D., Gordon, R.: Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems. SIAM Journal on Scientific Computing 27(3), 1092–1117 (2005) Liu et al. [2014] Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Liu, J., Wright, S.J., Sridhar, S.: An asynchronous parallel randomized kaczmarz algorithm. arXiv preprint arXiv:1401.4780 (2014) Recht et al. [2011] Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Recht, B., Re, C., Wright, S., Niu, F.: Hogwild!: A lock-free approach to parallelizing stochastic gradient descent. Advances in neural information processing systems 24 (2011) Chen [2018] Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Chen, X.: The Kaczmarz algorithm, row action methods, and statistical learning algorithms. Frames and harmonic analysis 706, 115–127 (2018) Needell et al. [2014] Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems 27 (2014) Cimmino [1938] Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Cimmino, G.: Cacolo approssimato per le soluzioni dei systemi di equazioni lineari. La Ricerca Scientifica (Roma) 1, 326–333 (1938) Guida and Sbordone [2023] Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Guida, M., Sbordone, C.: The Reflection Method for the Numerical Solution of Linear Systems. SIAM Review 65(4), 1137–1151 (2023) Gordon [2018] Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Gordon, D.: The Cimmino-Kaczmarz equivalence and related results. Applied Analysis and Optimization 2, 253–270 (2018) Agmon [1954] Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Agmon, S.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 382–392 (1954) Motzkin and Schoenberg [1954] Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Motzkin, T.S., Schoenberg, I.J.: The relaxation method for linear inequalities. Canadian Journal of Mathematics 6, 393–404 (1954) Hildreth [1957] Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Hildreth, C.: A quadratic programming procedure. Naval research logistics quarterly 4(1), 79–85 (1957) Jamil et al. [2015] Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Jamil, N., Chen, X., Cloninger, A.: Hildreth’s algorithm with applications to soft constraints for user interface layout. Journal of computational and applied mathematics 288, 193–202 (2015) Siddon [1985] Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Siddon, R.L.: Fast calculation of the exact radiological path for a three-dimensional CT array. Medical physics 12(2), 252–255 (1985) Gordon et al. [1970] Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of Theoretical Biology 29(3), 471–481 (1970) Herman and Lent [1976] Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Herman, G.T., Lent, A.: Iterative reconstruction algorithms. Computers in biology and medicine 6(4), 273–294 (1976) Andersen and Hansen [2014] Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Andersen, M.S., Hansen, P.C.: Generalized row-action methods for tomographic imaging. Numerical Algorithms 67(1), 121–144 (2014) Wu and Xiang [2020] Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Wu, N., Xiang, H.: Projected randomized Kaczmarz methods. Journal of Computational and Applied Mathematics 372, 112672 (2020) Gordon [2006] Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gordon, D.: Parallel art for image reconstruction in ct using processor arrays. The International Journal of Parallel, Emergent and Distributed Systems 21(5), 365–380 (2006) Gilbert [1972] Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
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- Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of theoretical biology 36(1), 105–117 (1972) Elfving et al. [2012] Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM Journal on Scientific Computing 34(4), 2000–2017 (2012) Andersen and Kak [1984] Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Andersen, A.H., Kak, A.C.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic imaging 6(1), 81–94 (1984) Hansen and Jørgensen [2018] Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Hansen, P.C., Jørgensen, J.S.: AIR Tools II: algebraic iterative reconstruction methods, improved implementation. Numerical Algorithms 79(1), 107–137 (2018) Hansen et al. [2021] Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Hansen, P.C., Jørgensen, J., Lionheart, W.R.: Computed tomography: algorithms, insight, and just enough theory. SIAM (2021) Wallace and Sekmen [2014] Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014) Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)
- Wallace, T., Sekmen, A.: Deterministic versus randomized kaczmarz iterative projection. arXiv preprint arXiv:1407.5593 (2014)