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On LPMHSS-based iteration methods for a class of weakly nonlinear systems

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Abstract

In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.

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Acknowledgments

The authors would like to thank the anonymous referees for their helpful suggestions, which greatly improved the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, People’s Republic of China

    Cui-Xia Li & Shi-Liang Wu

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  1. Cui-Xia Li
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  2. Shi-Liang Wu
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Correspondence to Shi-Liang Wu.

Additional information

Communicated by Jinyun Yuan.

This research was supported by NSFC (No. 11301009), HASTIT (No. 17HASTIT012), Natural Science Foundations of Henan Province (No. 15A110007) and Project of Young Core Instructor of Universities in Henan Province (2015GGJS-003).

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Li, CX., Wu, SL. On LPMHSS-based iteration methods for a class of weakly nonlinear systems. Comp. Appl. Math. 37, 1232–1249 (2018). https://doi.org/10.1007/s40314-016-0395-8

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  • DOI: https://doi.org/10.1007/s40314-016-0395-8

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