Faster Randomized Block Kaczmarz Algorithms
نویسندگان
چکیده
منابع مشابه
Convergence Rates for Greedy Kaczmarz Algorithms, and Faster Randomized Kaczmarz Rules Using the Orthogonality Graph
The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a non-asymptotic convergence rate analysis for this algorithm, spurring numerous extensions and generalizations of the Kaczmarz method. Rather than the random...
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We show that the Sparse Kaczmarz method is a particular instance of the coordinate gradient method applied to an unconstrained dual problem corresponding to a regularized `1-minimization problem subject to linear constraints. Based on this observation and recent theoretical work concerning the convergence analysis and corresponding convergence rates for the randomized block coordinate gradient ...
متن کاملFaster Alternatives to the Randomized Extended Kaczmarz Algorithm
In this note we compare the randomized extended Kaczmarz (EK) algorithm and randomized coordinate descent (CD) for solving the full-rank overdetermined linear least-squares problem and prove that CD is always faster than EK. For the general least-squares problems, we show that running first CD to compute the residual and then standard Kaczmarz on the resulting consistent system is more efficien...
متن کاملRandomized Block Kaczmarz Method with Projection for Solving Least Squares
The Kaczmarz method is an iterative method for solving overcomplete linear systems of equations Ax = b. The randomized version of the Kaczmarz method put forth by Strohmer and Vershynin iteratively projects onto a randomly chosen solution space given by a single row of the matrix A and converges exponentially in expectation to the solution of a consistent system. In this paper we analyze two bl...
متن کاملConvergence Rates for Greedy Kaczmarz Algorithms, and Randomized Kaczmarz Rules Using the Orthogonality Graph
The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a non-asymptotic convergence rate analysis for this algorithm, spurring numerous extensions and generalizations of the Kaczmarz method. Rather than the random...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2019
ISSN: 0895-4798,1095-7162
DOI: 10.1137/19m1251643