A two-sweep shift-splitting iterative method for complex symmetric linear systems

AIMS Mathematics

Li-Tao Zhang¹  Yan-Ping Wang¹  Yi-Fan Zhang¹  Xian-Yu Zuo²  Shi-Liang Wu³  Tong-Xiang Gu⁴ 

[1] 1 School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, Henan, 450015, P. R. China;2 Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng, 475004, P. R. China;3 School of Mathematics, Yunnan Normal University Yunnan, 650500, P. R. China;4 Laboratory of Computationary Physics, Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing, 100088, P. R. China;

关键词: complex symmetric linear systems;    two-sweep shift-splitting;    convergence;    preconditioner;    eigenvalue;   

DOI  :  10.3934/math.2020127

来源: DOAJ

【 摘 要 】

Recently, Chen and Ma [21] constructed the generalized shift-splitting (GSS) preconditioner, and gave the corresponding theoretical analysis and numerical experiments. In this paper, based on the generalized shift-splitting (GSS) preconditioner, we generalize their algorithms and further study the two-sweep shift-splitting (TSSS) preconditioner for complex symmetric linear systems. Moreover, by similar theoretical analysis, we obtain that the two-sweep shift-splitting iterative method is unconditionally convergent. In finally, one example is provided to confirm the effectiveness.

【 授权许可】

Unknown