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A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems

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Abstract

We propose a variant of PMHSS iteration method for solving and preconditioning a class of complex symmetric indefinite linear systems. The unconditional convergence theory of this iteration method is proved, and the choice of quasi-optimal parameter is also discussed. The explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrix are derived. In addition, theoretical analyses show that all eigenvalues are linearly distributed in the unit circle under suitable conditions. Numerical experiments are reported to illustrate the effectiveness and robustness of the proposed method.

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The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors are very much indebted to Dr. Rui-Xia Li for her proofreading. They are also grateful to the anonymous referees for their valuable comments and suggestions which improved the quality of this paper.

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11901505, 11901324, 11771193), the Natural Science Foundation of Fujian Province (No. 2020J01906), the Key Scientific Research Project for Colleges and Universities of Henan Province (No. 19A110006) and Nanhu Scholar Program for Young Scholars of XYNU.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang, China

    Zhong Zheng

  2. School of Mathematics and Finance, Putian University, Putian, China

    Min-Li Zeng

  3. School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

    Guo-Feng Zhang

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  1. Zhong Zheng
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  2. Min-Li Zeng
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  3. Guo-Feng Zhang
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Correspondence to Min-Li Zeng.

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Zheng, Z., Zeng, ML. & Zhang, GF. A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems. Numer Algor 91, 283–300 (2022). https://doi.org/10.1007/s11075-022-01262-6

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  • DOI: https://doi.org/10.1007/s11075-022-01262-6

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