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The randomized version of the Kaczmarz method for the solution of linear systems is known to converge linearly in expectation.
Angenäherte Auflösung von Systemen linearer Gleichungen
S. Kaczmarz · 1937
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On approximate solutions of systems of linear inequalities
A. J. Hoffman · 1952
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The relaxation method for finding common points of convex sets and its application to the solution of problems in convex programming
L. M. Bregman · 1967
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Some continuity properties of polyhedral multifunctions
S. M. Robinson · 1981
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A multiprojection algorithm using Bregman projections in a product space
Y. Censor and T. Elfving · 1994
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On projection algorithms for solving convex feasibility problems
H. H. Bauschke and J. M. Borwein · 1996
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Convergence of Bregman projection methods for solving consistent convex feasibility problems in reflexive Banach spaces
Y. Alber and D. Butnariu · 1997
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Legendre functions and the method of random Bregman projections
H. H. Bauschke and J. M. Borwein · 1997
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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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Atomic decomposition by basis pursuit
S. S. Chen, D. L. Donoho, and M. A. Saunders · 1998
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Strong conical hull intersection property, bounded linear regularity, Jameson’s property (G), and error bounds in convex optimization
H. H. Bauschke, J. M. Borwein, and W. Li · 1999
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Proximity function minimization using multiple Bregman projections, with applications to split feasibility and Kullback-Leibler distance minimization
C. Byrne and Y. Censor · 2001
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Iterative oblique projection onto convex sets and the split feasibility problem
C. Byrne · 2002
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Bregman monotone optimization algorithms
H. H. Bauschke, J. M. Borwein, and P. L. Combettes · 2003
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A unified treatment of some iterative algorithms in signal processing and image reconstruction
C. Byrne · 2004
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The multiple-sets split feasibility problem and its applications for inverse problems
Y. Censor, T. Elfving, N. Kopf, and T. Bortfeld · 2005
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Several solution methods for the split feasibility problem
J. Zhao and Q. Yang · 2005
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Fast low-rank modifications of the thin singular value decomposition
M. Brand · 2006
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An iterative regularization method for the solution of the split feasibility problem in Banach spaces
F. Schöpfer, T. Schuster, and A. K. Louis · 2008
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Convergence of the linearized Bregman iteration for ℓ 1 \ell_{1} -norm minimization
J.-F. Cai, S. Osher, and Z. Shen · 2009
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Variational Analysis
R. T. Rockafellar and R. J.-B. Wets · 2009
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Strongly convex programming for exact matrix completion and robust principal component analysis
H. Zhang, J. F. Hui Cai, L. Cheng, and J. Zhu · 2012
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Augmented ℓ 1 \ell_{1} and nuclear-norm models with a globally linearly convergent algorithm
M. J. Lai and W. Yin · 2013
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A fast randomized Kaczmarz algorithm for sparse solutions of consistent linear systems
H. Mansour and O. Yilmaz · 2013
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Randomized extended Kaczmarz for solving least squares
A. Zouzias and N. M. Freris · 2013
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Block Kaczmarz method with inequalities
J. Briskman and D. Needell · 2014
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The linearized Bregman method via split feasibility problems: Analysis and generalizations
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A randomized Kaczmarz algorithm with exponential convergence
T. Strohmer and R. Vershynin · 2009
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A singular value thresholding algorithm for matrix completion
J.-F. Cai, E. J. Candès, and Z. Shen · 2010
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Sparse and redundant representations: from theory to applications in signal and image processing
M. Elad · 2010
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Randomized methods for linear constraints: convergence rates and conditioning
D. Leventhal and A. S. Lewis · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. A. Parrilo · 2010
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Almost sure convergence of the Kaczmarz algorithm with random measurements
X. Chen and A. M. Powell · 2012
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D. A. Lorenz, F. Schöpfer, and S. Wenger · 2014
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A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing
D. A. Lorenz, S. Wenger, F. Schöpfer, and M. Magnor · 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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Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
P. Richtárik and M. Takáč · 2014
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Randomized Kaczmarz algorithms: Exact MSE analysis and optimal sampling probabilities
A. Agaskar, C. Wang, and Y. M. Lu · 2015
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Randomized sparse block Kaczmarz as randomized dual block-coordinate descent
S. Petra · 2015
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Bregman distances in inverse problems and partial differential equations
M. Burger · 2016
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Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm
D. Needell, N. Srebro, and R. Ward · 2016
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Linear convergence of descent methods for the unconstrained minimization of restricted strongly convex functions
F. Schöpfer · 2016
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Stochastic first-order methods with random constraint projection
M. Wang and D. P. Bertsekas · 2016
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