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We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems.
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M˜S Kaczmarz · 1937
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“Inexact Newton Methods”
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James˜W. Demmel · 1988
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Alan Edelman · 1992
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“Choosing the Forcing Terms in an Inexact Newton Method”
Stanley˜C. Eisenstat and Homer˜F. Walker · 1994
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“Iterative Methods for Linear and Nonlinear Equations”, Frontiers in Applied Mathematics 16
C.˜T. Kelley · 1995
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“Matrix Market : A Web Resource for Test Matrix Collections”
Ronald˜F Boisvert et al · 1997
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“An Inexact Interior Point Method”
S Bellavia · 1998
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“Iterative Methods for Sparse Linear Systems”
Y. Saad · 2003
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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”
Yoshua Bengio, Olivier Delalleau and Nicolas Le Roux · 2006
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Thomas Strohmer and Roman Vershynin · 2009
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D. Leventhal and A.˜S. Lewis · 2010
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“Randomized Kaczmarz solver for noisy linear systems”
D. Needell · 2010
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“A Newton-CG Augmented Lagrangian Method for Semidefinite Programming”
Xin-Yuan Zhao, Defeng Sun and Kim-Chuan Toh · 2010
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“Randomized Extended Kaczmarz for Solving Least-Squares”
Anastasios Zouzias and Nikolaos˜M Freris · 2013
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“CVX: Matlab Software for Disciplined Convex Programming, version 2.1”,
Michael Grant and Stephen Boyd · 2014
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“Krylov Subspace Methods : Principles and Analysis”
J“”org Liesen and Zdenek Strakos · 2014
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“Randomized Block Kaczmarz Method with Projection for Solving Least Squares”
Deanna Needell, Ran Zhao and Anastasios Zouzias · 2014
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“Coordinate descent with arbitrary sampling I: algorithms and complexity”
Zheng Qu and Richt“’arik · 2014
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“LIBSVM: A Library for Support Vector Machines”
Chih-Chung Chang and Chih-Jen Lin · 2011
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“Random Gradient-Free Minimization of Convex Functions”, 2011, pp. 1–34
Yurri Nesterov · 2011
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“Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method”
Deanna Needell and Joel˜A. Tropp · 2012
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“On the Randomized Kaczmarz Algorithm”
Liang Dai, Mojtaba Soltanalian and Kristiaan Pelckmans · 2013
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“Convergence Analysis of an Inexact Feasible Interior Point Method for Convex Quadratic Programming”
Jacek Gondzio · 2013
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Aaditya Ramdas · 2014
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“Optimization of Convex Functions with Random Pursuit”
S.˜U. Stich, C.˜L. M“”uller and B. G“”artner · 2014
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“Variable Metric Random Pursuit”
Sebastian˜U Stich · 2014
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“Convex Optimization with Random Pursuit”, 2014
Sebastian˜Urban Stich · 2014
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“Accelerated, Parallel and Proximal Coordinate Descent”
Olivier Fercoq and Peter Richt“’arik · 2015
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“Convergence Properties of the Randomized Extended Gauss-Seidel and Kaczmarz methods”
Anna Ma, Deanna Needell, Aaditya Ramdas and N˜A Mar · 2015
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“SDNA: Stochastic Dual Newton Ascent for Empirical Risk Minimization”
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