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We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system $Ax=b$.
Angenaherte auflsung 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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Image Reconstruction from Projections: The Fundamentals of Computerized Tomography
G. T. Herman · 1980
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Iterative algorithms for large partitioned linear systems, with applications to image reconstruction
P. P. B. Eggermont · 1981
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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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Parallel and distributed computation: numerical methods
D. P. Bertsekas and J. N. Tsitsiklis · 1989
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On the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data
L. Elsner, I. Koltracht, and M. Neumann · 1990
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Parallel variable distribution
M. C. Ferris and O. L. Mangasarian · 1994
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Characterization of the solutions set of least-squares problems by an extension of Kaczmarz’s projections method
C. Popa · 1999
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Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems
Y. Censor, D. Gordon, and R. Gordon · 2001
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G. T. Herman · 2009
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A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro · 2009
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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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Hogwild: A lock-free approach to parallelizing stochastic gradient descent
F. Niu, B. Recht, C. Ré, and S. J. Wright · 2011
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Introduction to the non-asymptotic analysis of random matrices
R. Vershynin · 2011
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Parallel coordinate descent methods for big data optimization
P. Richtárik and M. Takáč · 2012
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Randomized extended Kaczmarz for solving least-squares
A. Zouzias and N. M. Freris · 2012
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A randomized kaczmarz algorithm with exponential convergence
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Randomized methods for linear constraints: Convergence rates and conditioning
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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J. Liu and S. J. Wright · 2013
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An asynchronous parallel stochastic coordinate descent algorithm
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S. Sridhar, V. Bittorf, J. Liu, C. Zhang, C. Ré, and S. J. Wright · 2013
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