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Modified two-step scale-splitting iteration method for solving complex symmetric linear systems

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Abstract

For the large sparse complex symmetric linear systems, based on the combination method of real part and imaginary part method established by Wang et al. (J Comput Appl Math 325:188–197, 2017) and the double-step scale splitting one derived by Zheng et al. (Appl Math Lett 73:91–97, 2017), we construct a modified two-step scale-splitting (MTSS) iteration method in this paper. The convergence properties of the MTSS iteration method and its quasi-optimal parameters which minimizes the upper bound for the spectral radius of the proposed method are presented. Meanwhile, we derive the inexact variant of the MTSS iteration method. On this basis, we also introduce a minimum residual MTSS iteration method and its inexact version and give their convergence analyses. Numerical results on complex symmetric linear systems support that the proposed methods are more efficient and robust than some other commonly used ones.

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Acknowledgements

I would like to express my sincere thanks to the anonymous reviewers for their valuable suggestions and construct comments which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, People’s Republic of China

    Zheng-Ge Huang

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  1. Zheng-Ge Huang
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Correspondence to Zheng-Ge Huang.

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Communicated by Zhong-Zhi Bai.

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This research was supported by the National Natural Science Foundation of China (no. 11901123), the Guangxi Natural Science Foundation (no. 2018JJB110062, 2019AC20062) and the Xiangsihu Young Scholars Innovative Research Team of Guangxi University for Nationalities (no. 2019RSCXSHQN03)

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Huang, ZG. Modified two-step scale-splitting iteration method for solving complex symmetric linear systems. Comp. Appl. Math. 40, 122 (2021). https://doi.org/10.1007/s40314-021-01514-6

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  • DOI: https://doi.org/10.1007/s40314-021-01514-6

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