On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation

Author:

Xing Lili1ORCID,Bao Wendi1,Li Weiguo1ORCID

Affiliation:

1. College of Science, China University of Petroleum, Qingdao 266580, China

Abstract

A randomized block Kaczmarz method and a randomized extended block Kaczmarz method are proposed for solving the matrix equation AXB=C, where the matrices A and B may be full-rank or rank-deficient. These methods are iterative methods without matrix multiplication, and are especially suitable for solving large-scale matrix equations. It is theoretically proved that these methods converge to the solution or least-square solution of the matrix equation. The numerical results show that these methods are more efficient than the existing algorithms for high-dimensional matrix equations.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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