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Stochastic iterative algorithms have gained recent interest in machine learning and signal processing for solving large-scale systems of equations, $Ax=b$.
Angenäherte auflösung von systemen linearer gleichungen
S. Kaczmarz · 1937
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The relaxation method for linear inequalities
S. Agmon · 1954
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T. S. Motzkin and I. J. Schoenberg · 1954
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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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The relaxation method for solving systems of linear inequalities
J.-L. Goffin · 1980
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Row-action methods for huge and sparse systems and their applications
Y. Censor · 1981
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On the nonpolynomiality of the relaxation method for systems of linear inequalities
J.-L. Goffin · 1982
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On relaxation methods for systems of linear inequalities
J. Telgen · 1982
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Strong underrelaxation in Kaczmarz’s method for inconsistent systems
Y. Censor, P. P. B. Eggermont, and D. Gordon · 1983
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Block-iterative projection methods for parallel computation of solutions to convex feasibility problems
R. Aharoni and Y. Censor · 1989
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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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Projection algorithms for linear programming
U. Betke and P. Gritzmann · 1992
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Algebraic reconstruction techniques can be made computationally efficient
G. Herman and L. Meyer · 1993
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Å. Björck · 1996
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A fast Kaczmarz-Kovarik algorithm for consistent least-squares problems
C. Popa · 2001
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Relaxation, new combinatorial and polynomial algorithms for the linear feasibility problem
U. Betke · 2004
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A Kaczmarz-Kovarik algorithm for symmetric ill-conditioned matrices
C. Popa · 2004
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L. Xiao and S. Boyd · 2004
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S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah · 2006
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A randomized Kaczmarz algorithm with exponential convergence
T. Strohmer and R. Vershynin · 2009
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Randomized Kaczmarz solver for noisy linear systems
D. Needell · 2010
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Greedy gossip with eavesdropping
D. Ustebay, B. N. Oreshkin, M. J. Coates, and M. G. Rabbat · 2010
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A polynomial relaxation-type algorithm for linear programming
S. Chubanov · 2011
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The University of Florida sparse matrix collection
T. A. Davis and Y. Hu · 2011
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Acceleration of randomized Kaczmarz method via the Johnson-Lindenstrauss lemma
Y. C. Eldar and D. Needell · 2011
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Decentralized computation of effective resistances and acceleration of consensus algorithms
N. S. Aybat and M. Gürbüzbalaban · 2017
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A sampling Kaczmarz-Motzkin algorithm for linear feasibility
J. A. De Loera, J. Haddock, and D. Needell · 2017
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Privacy preserving randomized gossip algorithms
F. Hanzely, J. Konečnỳ, N. Loizou, P. Richtárik, and D. Grishchenko · 2017
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N. Loizou and P. Richtárik · 2017
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Randomized iterative methods with alternating projections
H. Xiang and L. Zhang · 2017
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Almost sure convergence of the Kaczmarz algorithm with random measurements
X. Chen and A. Powell · 2012
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On Kaczmarz’s projection iteration as a direct solver for linear least squares problems
C. Popa, T. Preclik, H. Köstler, and U. Rüde · 2012
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D. Needell and J. A. Tropp · 2013
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