The parameterized accelerated iteration method for solving the matrix equation AXB = C

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成果类型：

期刊论文

作者：

Tian, Zhaolu;Duan, Xuefeng;Wu, Nian-Ci;Liu, Zhongyun

通讯作者：

Tian, ZL

作者机构：

[Tian, Zhaolu] Shanxi Univ Finance & Econ, Coll Appl Math, Taiyuan 030006, Peoples R China.

[Duan, Xuefeng] Guilin Univ Elect Technol, Coll Math & Computat Sci, Guilin 541004, Peoples R China.

[Wu, Nian-Ci] South Cent Minzu Univ, Sch Math & Stat, Wuhan 430074, Peoples R China.

[Liu, Zhongyun] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410076, Peoples R China.

通讯机构：

[Tian, ZL ] S

Shanxi Univ Finance & Econ, Coll Appl Math, Taiyuan 030006, Peoples R China.

语种：

英文

关键词：

Matrix splitting;Optimal parameter;GBI method;Convergence;M-matrix

期刊：

Numerical Algorithms

ISSN：

1017-1398

年：

2023

页码：

1-25

DOI：

10.1007/s11075-023-01726-3

基金类别：

This work has been partially supported by the National Natural Science Foundation of China (12201651, 52263002, 12361079), the Natural Science Foundation of Shanxi Province (20210302123480), and the Research Project Supported by Shanxi Scholarship Council of China (2023-117).

机构署名：

本校为其他机构

院系归属：

数学与统计学院

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 $$AXB=C$$ . 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...

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The parameterized accelerated iteration method for solving the matrix equation AXB = C

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