Kaczmarz-Type Method for Solving Matrix Equation $AXB=C$
Numerical Analysis
2023-05-29 v1 Numerical Analysis
Abstract
In this paper, several row and column orthogonal projection methods are proposed for solving matrix equation , where the matrix and are full rank or rank deficient and equation is consistent or not. These methods are iterative methods without matrix multiplication. It is theoretically proved these methods converge to the solution or least-squares solution of the matrix equation. Numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrix.
Cite
@article{arxiv.2305.16684,
title = {Kaczmarz-Type Method for Solving Matrix Equation $AXB=C$},
author = {Xing Lili and Bao Wendi and Li Weiguo},
journal= {arXiv preprint arXiv:2305.16684},
year = {2023}
}