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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 AXB=CAXB=C, where the matrix AA and BB 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.

Keywords

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}
}
R2 v1 2026-06-28T10:47:12.592Z