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A preconditioner based on a splitting-type iteration method for solving complex symmetric indefinite linear systems

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Abstract

In this paper, we propose a preconditioned modified positive/negative-stable splitting (PMPNS) iteration method to solve complex symmetric indefinite linear system more efficiently. By analyzing the convergence of the PMPNS iteration method and discussing the spectral properties of the PMPNS iteration method, we construct a new preconditioner to make the eigenvalues of the coefficient matrix more aggregated, which leads to fast convergence of Krylov subspace iteration methods such as GMRES. Numerical example is given to illustrate the efficiency of the PMPNS preconditioner used in GMRES method. In particular, the GMRES method with the PMPNS preconditioner demonstrates meshsize-independent convergence behavior.

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Authors and Affiliations

  1. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Sciences, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Lu-Bin Cui

  2. School of Mathematics and Information Sciences, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Xiao-Qing Zhang & Yu-Tao Zheng

Authors
  1. Lu-Bin Cui
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  2. Xiao-Qing Zhang
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  3. Yu-Tao Zheng
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Correspondence to Lu-Bin Cui.

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This document is the results of the research project funded by National Natural Science Foundations of China (Nos. 11571095, 11601134), Foundation of Henan Educational Committee (No. 21A110013), Natural Science Foundations of Henan (No. 202300410236) and 2019 Scientific Research Project for Postgraduates of Henan Normal University (No. YL201920).

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Cui, LB., Zhang, XQ. & Zheng, YT. A preconditioner based on a splitting-type iteration method for solving complex symmetric indefinite linear systems. Japan J. Indust. Appl. Math. 38, 965–978 (2021). https://doi.org/10.1007/s13160-021-00471-1

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  • DOI: https://doi.org/10.1007/s13160-021-00471-1

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