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On GSOR-based iteration methods for solving weakly nonlinear systems with complex symmetric coefficient matrices

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Abstract

In this paper, two methods based on generalized successive overrelaxation (GSOR) for solving weakly nonlinear systems with complex coefficient matrices are proposed: Picard-accelerated GSOR (P-AGSOR) and Picard-preconditioned GSOR (P-PGSOR) methods. Theoretical analysis demonstrates the local convergence properties of the two methods under appropriate assumptions. Numerical examples confirm the effectiveness and superiority of the two methods.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Nanchang University, 999 Xuefu Road, Nanchang, 330031, People’s Republic of China

    Hui-Ting Wu, Xin Qi & Xiao-Yong Xiao

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  1. Hui-Ting Wu
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  2. Xin Qi
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  3. Xiao-Yong Xiao
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Correspondence to Xiao-Yong Xiao.

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This work is supported by National Nature Science Foundation of China with No. 12061048 and Nature Science Foundation of Jiangxi Province with No. 20181ACB20001.

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Wu, HT., Qi, X. & Xiao, XY. On GSOR-based iteration methods for solving weakly nonlinear systems with complex symmetric coefficient matrices. J. Appl. Math. Comput. 68, 601–621 (2022). https://doi.org/10.1007/s12190-021-01536-7

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  • DOI: https://doi.org/10.1007/s12190-021-01536-7

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