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Preconditioned triangular splitting iteration method for a class of complex symmetric linear systems

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Abstract

For the large sparse complex symmetric linear systems, we construct a preconditioned triangular splitting (PTS) iteration method based on utilizing the preconditioned technique and the triangular splitting of a matrix. Compared with the two-parameter two-step scale-splitting one established by Salkuyeh and Siahkolaei (Calcolo 55:8, 2018), PTS iteration method does not involve the complex arithmetic. The convergence theory of the PTS iteration method is established and the spectral properties of the PTS-preconditioned matrix are analyzed. In addition, by applying the minimum residual technique to the PTS iteration method, we develop the minimum residual PTS (MRPTS) iteration method to further improve the efficiency of the PTS one, then establish the corresponding convergence theory. Also, inexact version of the MRPTS iteration method and its convergence properties are presented. Numerical experiments are reported to verify the effectiveness of the proposed methods.

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Acknowledgements

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

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Authors and Affiliations

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

    Zheng-Ge Huang

  2. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Zhong Xu & Jing-Jing Cui

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  1. Zheng-Ge Huang
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  2. Zhong Xu
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  3. Jing-Jing Cui
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Correspondence to Zheng-Ge Huang.

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This research was supported by the National Natural Science Foundation of China (No. 10802068).

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Huang, ZG., Xu, Z. & Cui, JJ. Preconditioned triangular splitting iteration method for a class of complex symmetric linear systems. Calcolo 56, 22 (2019). https://doi.org/10.1007/s10092-019-0318-3

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