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

Li-Tao Zhang; Xian-Yu Zuo; Shi-Liang Wu; Tong-Xiang Gu; Yi-Fan Zhang; Yan-Ping Wang; Li-Tao Zhang; Xian-Yu Zuo; Shi-Liang Wu; Tong-Xiang Gu; Yi-Fan Zhang; Yan-Ping Wang

doi:10.3934/math.2020127

AIMS Mathematics

2020, Volume 5, Issue 3: 1913-1925. doi: 10.3934/math.2020127

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Research article

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

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

Received: 04 October 2019 Accepted: 06 February 2020 Published: 18 February 2020
MSC : 65F10, 65F15, 65F50

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.
- complex symmetric linear systems,
- two-sweep shift-splitting,
- convergence,
- preconditioner,
- eigenvalue
Citation: Li-Tao Zhang, Xian-Yu Zuo, Shi-Liang Wu, Tong-Xiang Gu, Yi-Fan Zhang, Yan-Ping Wang. A two-sweep shift-splitting iterative method for complex symmetric linear systems[J]. AIMS Mathematics, 2020, 5(3): 1913-1925. doi: 10.3934/math.2020127

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Abstract

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.

References

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