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S Karczmarz, Angenaherte auflosung von systemen linearer glei-chungen , Bull. Int. Acad. Pol. Sic. Let., Cl. Sci. Math. Nat. (1937), 355–357
1937
Earlier work this paper cites.
Shmuel Agmon, The relaxation method for linear inequalities , Canadian Journal of Mathematics 6
1954
Earlier work this paper cites.
Theodore Samuel Motzkin and Isaac Jacob Schoenberg, The relaxation method for linear inequalities , Canadian Journal of Mathematics 6
1954
Earlier work this paper cites.
R. K. Meany, A matrix inequality , SIAM Journal on Numerical Analysis 6
1969
Earlier work this paper cites.
Richard Gordon, Robert Bender, and Gabor T Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography , Journal of Theoretical Biology 29
1970
Earlier work this paper cites.
A Lent, Maximum entropy and multiplicative ART , Proc. Conf. Image Analysis and Evaluation, SPSE, Toronto, 1976
1976
Earlier work this paper cites.
Ahmed H Sameh and David J Kuck, On stable parallel linear system solvers , Journal of the ACM (JACM) 25
1978
Earlier work this paper cites.
Yair Censor, Row-action methods for huge and sparse systems and their applications , SIAM Review 23
1981
Earlier work this paper cites.
Sylvain Sardy, Andrew G Bruce, and Paul Tseng, Block coordinate relaxation methods for nonparametric wavelet denoising , Journal of computational and graphical statistics 9
2000
Earlier work this paper cites.

Similar

Yousef Saad, Iterative methods for sparse linear systems , vol. 82, SIAM, 2003
2003
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Thomas Strohmer and Roman Vershynin, A randomized Kaczmarz algorithm with exponential convergence , Journal of Fourier Analysis and Applications 15
2009
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Dennis Leventhal and Adrian S Lewis, Randomized methods for linear constraints: convergence rates and conditioning , Mathematics of Operations Research 35
2010
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Anastasios Zouzias and Nikolaos M Freris, Randomized extended Kaczmarz for solving least squares , SIAM Journal on Matrix Analysis and Applications 34
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2013
Cited alongside, same era.
Tim Wallace and Ali Sekmen, Deterministic versus randomized Kaczmarz iterative projection , arXiv preprint arXiv:1407.5593 (2014)
Original

Then

Julie Nutini, Behrooz Sepehry, Issam Laradji, Mark Schmidt, Hoyt Koepke, and Alim Virani, Convergence rates for greedy Kaczmarz algorithms, and faster randomized Kaczmarz rules using the orthogonality graph , arXiv preprint arXiv:1612.07838 (2016)
Original
2016
Later among the works it cites.
Zhong-Zhi Bai and Wen-Ting Wu, On greedy randomized Kaczmarz method for solving large sparse linear systems , SIAM Journal on Scientific Computing 40
2018
Later among the works it cites.
Jamie Haddock and Anna Ma, Greed works: An improved analysis of sampling Kaczmarz-Motkzin , arXiv preprint arXiv:1912.03544 (2019)
Original
2019
Later among the works it cites.
Vivak Patel, Mohammad Jahangoshahi, and Daniel Adrian Maldonado, An implicit representation and iterative solution of randomly sketched linear systems , arXiv preprint arXiv:1904.11919 (2019)
Original
2019
Later among the works it cites.

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2021

Convergence of Adaptive, Randomized, Iterative Linear Solvers

Patel, Vivak, Jahangoshahi, Mohammad, Maldonado, Daniel Adrian

Understand

Deterministic and randomized, row-action and column-action linear solvers have become increasingly popular owing to their simplicity, low computational and memory complexities, and ease of composition with other techniques.

Moreover, in order to achieve high-performance, such solvers must often be adapted to the given problem structure and to the hardware platform on which the problem will be solved.
Unfortunately, determining whether such adapted solvers will converge to a solution has required equally unique analyses.
As a result, adapted, reliable solvers are slow to be developed and deployed.

Built on

S Karczmarz, Angenaherte auflosung von systemen linearer glei-chungen , Bull. Int. Acad. Pol. Sic. Let., Cl. Sci. Math. Nat. (1937), 355–357
1937
Earlier work this paper cites.
Shmuel Agmon, The relaxation method for linear inequalities , Canadian Journal of Mathematics 6
1954
Earlier work this paper cites.
Theodore Samuel Motzkin and Isaac Jacob Schoenberg, The relaxation method for linear inequalities , Canadian Journal of Mathematics 6
1954
Earlier work this paper cites.
R. K. Meany, A matrix inequality , SIAM Journal on Numerical Analysis 6
1969
Earlier work this paper cites.
Richard Gordon, Robert Bender, and Gabor T Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography , Journal of Theoretical Biology 29
1970
Earlier work this paper cites.
A Lent, Maximum entropy and multiplicative ART , Proc. Conf. Image Analysis and Evaluation, SPSE, Toronto, 1976
1976
Earlier work this paper cites.
Ahmed H Sameh and David J Kuck, On stable parallel linear system solvers , Journal of the ACM (JACM) 25
1978
Earlier work this paper cites.
Yair Censor, Row-action methods for huge and sparse systems and their applications , SIAM Review 23
1981
Earlier work this paper cites.
Sylvain Sardy, Andrew G Bruce, and Paul Tseng, Block coordinate relaxation methods for nonparametric wavelet denoising , Journal of computational and graphical statistics 9
2000
Earlier work this paper cites.

Similar

Yousef Saad, Iterative methods for sparse linear systems , vol. 82, SIAM, 2003
2003
Cited alongside, same era.
Thomas Strohmer and Roman Vershynin, A randomized Kaczmarz algorithm with exponential convergence , Journal of Fourier Analysis and Applications 15
2009
Cited alongside, same era.
Dennis Leventhal and Adrian S Lewis, Randomized methods for linear constraints: convergence rates and conditioning , Mathematics of Operations Research 35
2010
Cited alongside, same era.
Anastasios Zouzias and Nikolaos M Freris, Randomized extended Kaczmarz for solving least squares , SIAM Journal on Matrix Analysis and Applications 34
Original
2013
Cited alongside, same era.
Tim Wallace and Ali Sekmen, Deterministic versus randomized Kaczmarz iterative projection , arXiv preprint arXiv:1407.5593 (2014)
Original

Then

Julie Nutini, Behrooz Sepehry, Issam Laradji, Mark Schmidt, Hoyt Koepke, and Alim Virani, Convergence rates for greedy Kaczmarz algorithms, and faster randomized Kaczmarz rules using the orthogonality graph , arXiv preprint arXiv:1612.07838 (2016)
Original
2016
Later among the works it cites.
Zhong-Zhi Bai and Wen-Ting Wu, On greedy randomized Kaczmarz method for solving large sparse linear systems , SIAM Journal on Scientific Computing 40
2018
Later among the works it cites.
Jamie Haddock and Anna Ma, Greed works: An improved analysis of sampling Kaczmarz-Motkzin , arXiv preprint arXiv:1912.03544 (2019)
Original
2019
Later among the works it cites.
Vivak Patel, Mohammad Jahangoshahi, and Daniel Adrian Maldonado, An implicit representation and iterative solution of randomly sketched linear systems , arXiv preprint arXiv:1904.11919 (2019)
Original
2019
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2014

Cited alongside, same era.

Robert M Gower and Peter Richtárik, Randomized iterative methods for linear systems , SIAM Journal on Matrix Analysis and Applications 36

2015

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Anna Ma, Deanna Needell, and Aaditya Ramdas, Convergence Properties of the Randomized Extended Gauss-Seidel and Kaczmarz Methods , SIAM Journal on Matrix Analysis and Applications 36

2015

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Deanna Needell, Nathan Srebro, and Rachel Ward, Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm , Mathematical Programming 155

2016

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Yi-Shu Du, Ken Hayami, Ning Zheng, Keiichi Morikuni, and Jun-Feng Yin, Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems , arXiv preprint arXiv:2006.10818 (2020)

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Richard Tran Mills, Mark F Adams, Satish Balay, Jed Brown, Alp Dener, Matthew Knepley, Scott E Kruger, Hannah Morgan, Todd Munson, Karl Rupp, et al., Toward performance-portable PETSc for GPU-based exascale systems , arXiv preprint arXiv:2011.00715 (2020)

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2020

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Peter Richtárik and Martin Takác, Stochastic reformulations of linear systems: algorithms and convergence theory , SIAM Journal on Matrix Analysis and Applications 41

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Stefan Steinerberger, A weighted randomized kaczmarz method for solving linear systems , arXiv preprint arXiv:2007.02910 (2020)

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