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Two-parameter double-step scale splitting real-valued iterative method for solving complex symmetric linear systems

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Abstract

In this work, we first apply the parameter accelerating strategy to the double-step scale splitting (DSS) real-valued algorithm one derived by Zhang et al. (Appl Math Comput 353: 338–346, 2019) and establish a two-parameter DSS real-valued (TDSS) iterative method for solving the large sparse complex symmetric linear systems. Furthermore, we explore the convergence conditions of this method. Moreover, we derive the optimal parameters which minimize an upper bound of the spectral radius of the iteration matrix for the TDSS iterative method. In addition, by utilizing the latest information of the TDSS iterative scheme, we deduce an improved TDSS (ITDSS) iterative method and analyze its convergence properties. At last, the correctness of the theories and the advantages of the ITDSS iterative method over some existing ones are verified by three numerical experiments.

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Acknowledgements

We would like to express our sincere thanks to editor and anonymous reviewers for their valuable suggestions and constructive comments which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, People’s Republic of China

    Xiaofeng Xie, Zhengge Huang, Jingjing Cui & Beibei Li

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  1. Xiaofeng Xie
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  2. Zhengge Huang
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  3. Jingjing Cui
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Correspondence to Zhengge Huang.

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This work was supported by the National Science Foundation of China (No. 11901123), the Guangxi Natural Science Foundations (No. 2019AC20062, 2018JJB110062, 2021JJB110006, 2021AC19147), the Natural Science Foundation of Guangxi University for Nationalities (No. 2019KJQN001) and the Graduate Innovation Program of Guangxi University for Nationalities (No. gxun-chxs 2021056).

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Xie, X., Huang, Z., Cui, J. et al. Two-parameter double-step scale splitting real-valued iterative method for solving complex symmetric linear systems. Japan J. Indust. Appl. Math. 40, 1125–1157 (2023). https://doi.org/10.1007/s13160-023-00569-8

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