Two Quasi-combining Real and Imaginary Parts Iteration Methods for Solving Complex Symmetric System of Linear Equations

doi:10.1007/s42967-024-00448-0

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (2): 427-455.doi: 10.1007/s42967-024-00448-0

Two Quasi-combining Real and Imaginary Parts Iteration Methods for Solving Complex Symmetric System of Linear Equations

Bei-Bei Li, Jing-Jing Cui, Zheng-Ge Huang, Xiao-Feng Xie

College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, Guangxi, China

收稿日期:2024-01-27 修回日期:2024-07-08 出版日期:2026-04-07 发布日期:2026-04-07
通讯作者: Jing-Jing Cui,E-mail:jingjingcui1990@163.com E-mail:jingjingcui1990@163.com
基金资助:
This work was subsidized by the National Natural Science Foundation of China (No. 12361078) and the Guangxi Natural Science Foundation of China (Nos. 2018JJB110062, 2019AC20062, 2021JJB110006, and 2021AC19147).

Two Quasi-combining Real and Imaginary Parts Iteration Methods for Solving Complex Symmetric System of Linear Equations

Bei-Bei Li, Jing-Jing Cui, Zheng-Ge Huang, Xiao-Feng Xie

College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, Guangxi, China

Received:2024-01-27 Revised:2024-07-08 Online:2026-04-07 Published:2026-04-07
Contact: Jing-Jing Cui,E-mail:jingjingcui1990@163.com E-mail:jingjingcui1990@163.com
Supported by:
This work was subsidized by the National Natural Science Foundation of China (No. 12361078) and the Guangxi Natural Science Foundation of China (Nos. 2018JJB110062, 2019AC20062, 2021JJB110006, and 2021AC19147).

摘要/Abstract

摘要： To solve the large sparse complex symmetric linear equations more efficiently, we introduce a new matrix \begin{document}$ H_\omega =W+\omega T $\end{document} and establish two quasi-combining real and imaginary parts iteration methods, which will be simply called the QCRI1 and QCRI2 iteration methods. We give the upper bounds of the spectral radiuses of the two methods and discuss their convergence conditions that make these upper bounds less than 1. In addition, the theoretical quasi-optimal parameters minimizing the upper bound of the spectral radius of the iteration matrix of the QCRI1 method are presented. Meanwhile, the inexact versions of the proposed methods are also provided, and their convergence properties are given. Finally, numerical results illustrate the effectiveness of our methods.

关键词: Complex symmetric linear system, Hermitian and skew-Hermitian splitting, Iteration method, Convergence property, Inexact implementation

Abstract: To solve the large sparse complex symmetric linear equations more efficiently, we introduce a new matrix \begin{document}$ H_\omega =W+\omega T $\end{document} and establish two quasi-combining real and imaginary parts iteration methods, which will be simply called the QCRI1 and QCRI2 iteration methods. We give the upper bounds of the spectral radiuses of the two methods and discuss their convergence conditions that make these upper bounds less than 1. In addition, the theoretical quasi-optimal parameters minimizing the upper bound of the spectral radius of the iteration matrix of the QCRI1 method are presented. Meanwhile, the inexact versions of the proposed methods are also provided, and their convergence properties are given. Finally, numerical results illustrate the effectiveness of our methods.

Key words: Complex symmetric linear system, Hermitian and skew-Hermitian splitting, Iteration method, Convergence property, Inexact implementation

中图分类号:

Bei-Bei Li, Jing-Jing Cui, Zheng-Ge Huang, Xiao-Feng Xie. Two Quasi-combining Real and Imaginary Parts Iteration Methods for Solving Complex Symmetric System of Linear Equations[J]. Communications on Applied Mathematics and Computation, 2026, 8(2): 427-455.

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Two Quasi-combining Real and Imaginary Parts Iteration Methods for Solving Complex Symmetric System of Linear Equations

Two Quasi-combining Real and Imaginary Parts Iteration Methods for Solving Complex Symmetric System of Linear Equations

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