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The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints.
Angenäherte Auflösung von Systemen linearer Gleichungen, Bulletin International de l’Académie Polonaise des Sciences et des Letters
S. Kaczmarz · 1937
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On approximate solutions of systems of linear inequalities
A. J. Hoffman · 1952
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On convergence proofs for perceptrons
A. B. J. Novikoff · 1962
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Two algorithms related to the method of steepest descent
T. Whitney and R. Meany · 1967
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Condition numbers and equilibrium of matrices
A. van der Sluis · 1969
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Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and x-ray photography
R. Gordon, R. Bender, and G. T. Herman · 1970
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Projection method for solving a singular system of linear equations and its applications
K. Tanabe · 1971
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Row-action methods for huge and sparse systems and their applications
Y. Censor · 1981
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Strong underrelaxation in Kaczmarz’s method for inconsistent systems
Y. Censor, P. B. Eggermont, and D. Gordon · 1983
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Extensions of Lipchitz mappings into a Hilbert space
W. B. Johnson and J. Lindenstrauss · 1984
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Rate of convergence of the method of alternating projections
F. Deutsch · 1985
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On the acceleration of Kaczmarz’s method for inconsistent linear systems
M. Hanke and W. Niethammer · 1990
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New variants of the POCS method using affine subspaces of finite codimension with applications to irregular sampling
H. G. Feichtinger, C. Cenker, M. Mayer, H. Steier, and T. Strohmer · 1992
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Algebraic reconstruction techniques can be made computationally efficient
G. T. Herman and L. B. Meyer · 1993
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The rate of convergence for the method of alternating projections, II
F. Deutsch and H. Hundal · 1997
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Learning with local and global consistency
D. Zhou, O. Bousquet, T. N. Lal, J. Weston, and B. Schölkopf · 2004
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On the rate of convergence of the alternating projection method in finite dimensional spaces
A. Galántai · 2005
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Gaussian Markov Random Fields: Theory and Applications
H. Rue and L. Held · 2005
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Label propagation and quadratic criterion
Y. Bengio, O. Delalleau, and N. Le Roux · 2006
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Minimizing finite sums with the stochastic average gradient
M. Schmidt, N. Le Roux, and F. Bach · 2013
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L x = b {L}x=b Laplacian solvers and their algorithmic applications
N. K. Vishnoi · 2013
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Randomized extended Kaczmarz for solving least-squares
A. Zouzias and N. M. Freris · 2013
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An accelerated randomized Kaczmarz method
J. Liu and S. J. Wright · 2014
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Paved with good intentions: Analysis of a randomized block Kaczmarz method
D. Needell and J. A. Tropp · 2014
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Randomized iterative methods for linear systems
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A note on the behaviour of the randomized Kaczmarz algorithm of Strohmer and Vershynin
Y. Censor, G. T. Herman, and M. Jiang · 2009
Cited alongside, same era.
A randomized Kaczmarz algorithm with exponential convergence
T. Strohmer and R. Vershynin · 2009
Cited alongside, same era.
Randomized methods for linear constraints: convergence rates and conditioning
L. Leventhal and A. S. Lewis · 2010
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Randomized Kaczmarz solver for noisy linear systems
D. Needell · 2010
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Acceleration of randomized Kaczmarz methods via the Johnson-Lindenstrauss Lemma
Y. C. Eldar and D. Needell · 2011
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Greedy and randomized versions of the multiplicative Schwartz method
M. Griebel and P. Oswald · 2012
Cited alongside, same era.
R. M. Gower and P. Richtárik · 2015
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Convergence properties of the randomized extended Gauss-Seidel and Kaczmarz methods
A. Ma, D. Needell, and A. Ramdas · 2015
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Stochastic gradient descent and the randomized Kaczmarz algorithm
D. Needell, N. Srebro, and R. Ward · 2015
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Coordinate descent converges faster with the Gauss-Southwell rule than random selection
J. Nutini, M. Schmidt, I. H. Laradji, M. Friedlander, and H. Koepke · 2015
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Convergence analysis for Kaczmarz-type methods in a Hilbert space framework
P. Oswald and W. Zhou · 2015
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S. J. Wright · 2015
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Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition
H. Karimi, J. Nutini, and M. Schmidt · 2016
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Finding a maximum weight sequence with dependency constraints
B. Sepehry · 2016
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