Single step real-valued iterative method for linear system of equations with complex symmetric matrices

Jingjing Cui; Zhengge Huang; Beibei Li; Xiaofeng Xie

doi:10.4134/BKMS.b220524

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(5): 1181-1199

Online first article September 6, 2023 Printed September 30, 2023

https://doi.org/10.4134/BKMS.b220524

Single step real-valued iterative method for linear system of equations with complex symmetric matrices

Jingjing Cui, Zhengge Huang, Beibei Li, Xiaofeng Xie

Guangxi Minzu University; Guangxi Minzu University; Guangxi Minzu University; Guangxi Minzu University

Abstract

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Abstract

For solving complex symmetric positive definite linear systems, we propose a single step real-valued (SSR) iterative method, which does not involve the complex arithmetic. The upper bound on the spectral radius of the iteration matrix of the SSR method is given and its convergence properties are analyzed. In addition, the quasi-optimal parameter which minimizes the upper bound for the spectral radius of the proposed method is computed. Finally, numerical experiments are given to demonstrate the effectiveness and robustness of the propose methods.

Keywords: Symmetric positive semi-definite, symmetric positive definite, system of linear equations, SSR iteration method

MSC numbers: Primary 65F99

Supported by: This work was financially supported by the Guangxi Natural Science Foundations (No.2021GXNSFBA196064, Guike AD21220129), the National Science Foundation of China (No.11901123), and the Guangxi Natural Science Foundations (2019GXNSFBA185014, Guike AD20159056).