Kaczmarz-type methods for solving matrix equations

被引：0

作者：

Li, Weiguo ^{[1
]}

Bao, Wendi ^{[1
]}

Xing, Lili ^{[1
]}

Guo, Zhiwei ^{[1
]}

机构：

[1] China Univ Petr, Coll Sci, Qingdao 266580, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2024年 / 101卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Kaczmarz method; coordinate-descent method; convergence; matrix equation; inverse; CONVERGENCE-RATES;

D O I：

10.1080/00207160.2024.2372420

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：708 / 731

页数：24

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