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

Lili Xing; Wendi Bao; Weiguo Li

doi:10.20944/preprints202310.0686.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 10 October 2023 / Approved: 11 October 2023 / Online: 11 October 2023 (07:42:21 CEST)

Randomized block Kaczmarz Method and randomized extended block Kaczmarz Method are proposed for solving matrix equation AXB=C, where the matrix 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 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.

matrix equation; randomized block Kaczmarz; randomized extended block Kaczmarz; convergence

Computer Science and Mathematics, Computational Mathematics

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

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