Kaczmarz-type methods for solving matrix equations

Abstract

In this paper, several Kaczmarz-type numerical methods for solving the matrix equations AX = B and XA = C are proposed, where the coefficient matrix A may be full rank or deficient rank. These methods are iterative methods without matrix multiplication. Theoretically, the convergence of these methods is proved. The numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrices.

Keywords:

• Kaczmarz method
• coordinate-descent method
• convergence
• matrix equation
• inverse

2020 Mathematics Subject Classifications:

• 65F05
• 65F10
• 65F30
• 65F45

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This article was supported by the National Natural Science Foundation of China [grant number 61931025] and the National Natural Science Foundation of China [grant number 42374156].