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

doi:10.1007/s42967-024-00448-0

Abstract

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

CLC Number:

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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