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The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations.
Angenäherte auflösung von systemen linearer gleichungen
Stefan M. Kaczmarz · 1937
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A stochastic approximation method
Herbert Robbins and Sutton Monro · 1951
Earlier work this paper cites.
Algebraic reconstruction techniques (art) for three-dimensional electron microscopy and x-ray photography
Richard Gordon, Robert Bender, and Gabor T Herman · 1970
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The angles between the null spaces of x rays
Ch Hamaker and DC Solmon · 1978
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Block-iterative methods for consistent and inconsistent linear equations
Tommy Elfving · 1980
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Iterative algorithms for large partitioned linear systems, with applications to image reconstruction
Paulus Petrus Bernardus Eggermont, Gabor T Herman, and Arnold Lent · 1981
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Block-iterative projection methods for parallel computation of solutions to convex feasibility problems
Ron Aharoni and Yair Censor · 1989
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On the acceleration of Kaczmarz’s method for inconsistent linear systems
Martin Hanke and Wilhelm Niethammer · 1990
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On the use of small relaxation parameters in Kaczmarz method
Martin Hanke and Wilhelm Niethammer · 1990
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Algebraic reconstruction techniques can be made computationally efficient (positron emission tomography application)
Gabor T. Herman and Lorraine B. Meyer · 1993
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Online algorithms and stochastic approximations
Léon Bottou · 1998
Earlier work this paper cites.
The method of alternating projections and the method of subspace corrections in hilbert space
Jinchao Xu and Ludmil Zikatanov · 2002
Cited alongside, same era.
Component-averaged row projections: A robust, block-parallel scheme for sparse linear systems
Dan Gordon and Rachel Gordon · 2005
Cited alongside, same era.
Applied iterative methods
Charles L Byrne · 2007
Cited alongside, same era.
A randomized Kaczmarz algorithm with exponential convergence
Thomas Strohmer and Roman Vershynin · 2009
Cited alongside, same era.
Randomized methods for linear constraints: convergence rates and conditioning
Dennis Leventhal and Adrian S Lewis · 2010
Cited alongside, same era.
Randomized Kaczmarz solver for noisy linear systems
Deanna Needell · 2010
Cited alongside, same era.
Paved with good intentions: Analysis of a randomized block Kaczmarz method
Deanna Needell and Joel A. Tropp · 2012
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Two-subspace projection method for coherent overdetermined systems
Deanna Needell and Rachel Ward · 2013
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Randomized extended Kaczmarz for solving least squares
Anastasios Zouzias and Nikolaos M. Freris · 2013
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An asynchronous parallel randomized Kaczmarz algorithm
Ji Liu, Stephen J. Wright, and Sridhar Srikrishna · 2014
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Randomized iterative methods for linear systems
Robert M. Gower and Peter Richtárik · 2015
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Acceleration of randomized kaczmarz method via the johnson–lindenstrauss lemma
Yonina C Eldar and Deanna Needell · 2011
Cited alongside, same era.
HOGWILD!: A lock-free approach to parallelizing stochastic gradient descent
Feng Niu, Benjamin Recht, Christopher Ré, and Stephen J. Wright · 2011
Cited alongside, same era.
Exponential convergence of a randomized Kaczmarz algorithm with relaxation
Yong Cai, Yang Zhao, and Yuchao Tang · 2012
Cited alongside, same era.
Almost sure convergence of the kaczmarz algorithm with random measurements
Xuemei Chen and Alexander M Powell · 2012
Cited alongside, same era.
Anna Ma, Deanna Needell, and Aaditya Ramdas · 2015
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Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm
Deanna Needell, Nathan Srebro, and Rachel Ward · 2015
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Block stochastic gradient iteration for convex and nonconvex optimization
Yangyang Xu and Wotao Yin · 2015
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Batched stochastic gradient descent with weighted sampling
Deanna Needell and Rachel Ward · 2017
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Stochastic reformulations of linear systems: Algorithms and convergence theory
Peter Richtárik and Martin Takáč · 2017
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