The parameterized accelerated iteration method for solving the matrix equation AXB=C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$AXB=C$$\end{document}

被引：0
作者：
Zhaolu Tian [1 ]
Xuefeng Duan [2 ]
Nian-Ci Wu [3 ]
Zhongyun Liu [4 ]
机构：
[1] Shanxi University of Finance and Economics,College of Applied Mathematics
[2] Guilin University of Electronic and Technology,College of Mathematics and Computational Science
[3] South-Central Minzu University,School of Mathematics and Statistics
[4] Changsha University of Science and Technology,School of Mathematics and Statistics
来源：
Numerical Algorithms | 2024年 / 97卷 / 2期
关键词：
Matrix splitting; Optimal parameter; GBI method; Convergence; -matrix;
D O I：
10.1007/s11075-023-01726-3
中图分类号：
学科分类号：
摘要：
By introducing two parameters in the splittings of the matrices A and B, this paper presents a parameterized accelerated iteration (PAI) method for solving the matrix equation AXB=C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$AXB=C$$\end{document}. The convergence property of the PAI method and the choices of the parameters are thoroughly investigated. Additionally, based on some special splittings of the matrices A and B, several variants of the PAI method are established. Furthermore, for some certain cases, the optimal parameters can be determined, and it is demonstrated that the PAI method is more efficient than the gradient-based iteration (GBI) method (Ding et al. Appl. Math. Comput. 197, 41–50 2008). Finally, by comparing it with several existing iteration methods, the effectiveness of the PAI method is verified through four numerical examples.
引用
收藏
页码：843 / 867
页数：24
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