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A fully structured preconditioner for a class of complex symmetric indefinite linear systems

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Abstract

Based on the equivalent transformation of the complex coefficient matrix, a fully structured preconditioner which is economic to implement within GMRES acceleration is presented for solving a class of complex symmetric indefinite linear systems. We analyze the computational complexity of the proposed preconditioner and show that all eigenvalues of the corresponding preconditioned matrix are clustered at a top half annulus. Compared with some other existing preconditioners, the validity of theoretical analysis and the effectiveness of the proposed preconditioner are verified by numerical experiments.

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, People’s Republic of China

    Zhong Zheng & Yue-Fen Chen

  2. College of Information Engineering, Xinyang Agriculture and Forestry University, Xinyang, People’s Republic of China

    Jing Chen

Authors
  1. Zhong Zheng
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  2. Jing Chen
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  3. Yue-Fen Chen
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Correspondence to Zhong Zheng.

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Communicated by Lothar Reichel.

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This work is supported by the National Natural Science Foundation of China (No. 11901505), Natural Science Foundation of Henan (No. 202300410343), the Key Scientific Research Project for Colleges and Universities of Henan Province (No. 19A110006), the Training Plan of Young Key Teachers in Universities of Henan Province (No. 2018GGJS096) and Nanhu Scholar Program for Young Scholars of XYNU.

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Zheng, Z., Chen, J. & Chen, YF. A fully structured preconditioner for a class of complex symmetric indefinite linear systems. Bit Numer Math 62, 667–680 (2022). https://doi.org/10.1007/s10543-021-00887-8

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