On Greedy Randomized Kaczmarz Method for Solving Large Sparse Linear Systems

For solving large-scale systems of linear equations by iteration methods, we introduce an effective probability criterion for selecting the working rows from the coefficient matrix and construct a ...

[1]  Y. Censor.  Row-Action Methods for Huge and Sparse Systems and Their Applications , 1981 .

[2]  R. Vershynin,et al.  A Randomized Kaczmarz Algorithm with Exponential Convergence , 2007, math/0702226.

[3]  Deanna Needell,et al.  Convergence Properties of the Randomized Extended Gauss-Seidel and Kaczmarz Methods , 2015, SIAM J. Matrix Anal. Appl..

[4]  Marcus A. Magnor,et al.  A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing , 2014, 2014 IEEE International Conference on Image Processing (ICIP).

[5]  R B Guenther,et al.  Reconstruction of objects from radiographs and the location of brain tumors. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Zhong-Zhi Bai,et al.  On the Meany inequality with applications to convergence analysis of several row-action iteration methods , 2013, Numerische Mathematik.

[7]  Yair Censor,et al.  Parallel application of block-iterative methods in medical imaging and radiation therapy , 1988, Math. Program..

[8]  S. McCormick.  An iterative procedure for the solution of constrained nonlinear equations with application to optimization problems , 1975 .

[9]  Rafal Zdunek,et al.  Kaczmarz extended algorithm for tomographic image reconstruction from limited-data , 2004, Math. Comput. Simul..

[10]  Nikolaos V. Sahinidis,et al.  GPU computing with Kaczmarz's and other iterative algorithms for linear systems , 2010, Parallel Comput..

[11]  Peter Richtárik,et al.  Stochastic Dual Ascent for Solving Linear Systems , 2015, ArXiv.

[12]  G. Herman,et al.  Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. , 1970, Journal of theoretical biology.

[13]  A. Lent,et al.  Iterative algorithms for large partitioned linear systems, with applications to image reconstruction , 1981 .

[14]  Miroslav Rozlozník,et al.  On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems , 2015, SIAM J. Numer. Anal..

[15]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[16]  Claude Brezinski,et al.  Projection methods for systems of equations , 1997 .