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Shift-splitting fixed point iteration method for solving generalized absolute value equations

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Abstract

Using the shift-splitting strategy, we propose a shift-splitting fixed point iteration (FPI-SS) method for solving large sparse generalized absolute value equations (GAVEs). The FPI-SS method is based on reformulating the GAVE as a two-by-two block nonlinear equation. Several different types of convergence conditions of the FPI-SS method are presented under suitable restrictions. Through numerical experiments, we demonstrate that the FPI-SS method is superior to the fixed point iteration method and the SOR-like iteration method in computing efficiency.

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Acknowledgements

The authors would like to thank the two referees for their constructive suggestions which greatly improve the presentation of the paper. This research was funded by the Natural Science Foundation of Gansu Province (No. 20JR5RA464) and the National Natural Science Foundation of China (Nos. 11501272 and 11901267).

Funding

The research of Xu Li was supported by the Natural Science Foundation of Gansu Province (No. 20JR5RA464) and the National Natural Science Foundation of China (No. 11501272). The research of Yi-Xin Li was supported by the Natural Science Foundation of Gansu Province (No. 20JR5RA464). The research of Yan Dou was supported by the National Natural Science Foundation of China (No. 11901267).

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Authors and Affiliations

  1. Department of Applied Mathematics, Lanzhou University of Technology, 730050, Lanzhou, People’s Republic of China

    Xu Li, Yi-Xin Li & Yan Dou

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  1. Xu Li
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  2. Yi-Xin Li
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  3. Yan Dou
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Contributions

Xu Li and Yi-Xin Li wrote the main manuscript text and Yi-Xin Li performed the numerical experiments. All authors reviewed the manuscript.

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Correspondence to Xu Li.

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Li, X., Li, YX. & Dou, Y. Shift-splitting fixed point iteration method for solving generalized absolute value equations. Numer Algor 93, 695–710 (2023). https://doi.org/10.1007/s11075-022-01435-3

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  • DOI: https://doi.org/10.1007/s11075-022-01435-3

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