Abstract
In this paper, we investigate the iterative methods for solving the absolute value equations (AVEs). Using matrix splitting and the relaxed technique, a relaxed-based matrix splitting (RMS) method is presented. As special cases, we propose a relaxed-based Picard (RP) method, relaxed-based AOR (RAOR) method, and relaxed-based SOR (RSOR) method. These methods include some known methods as special cases, such as the Newton-based matrix splitting iterative method, the modified Newton type iteration method, the Picard method, a new SOR-like method, the fixed point iteration method, the SOR-like method, the AOR method, the modified SOR-like method, etc. Some convergence conditions of the proposed method are presented. Numerical examples verify the theoretical results and the advantages of the new methods.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11771213 and 11971242), the Priority Academic Program Development of Jiangsu Higher Education Institutions, and Wuxi University Research Start-up Fund for Introduced Talents. The authors would like to thank the referees for their many valuable suggestions and comments which led us to improve this paper.
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Communicated by Jinyun Yuan.
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Song, J., Song, Y. Relaxed-based matrix splitting methods for solving absolute value equations. Comp. Appl. Math. 42, 19 (2023). https://doi.org/10.1007/s40314-022-02157-x
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DOI: https://doi.org/10.1007/s40314-022-02157-x
Keywords
- Absolute value equations
- Relaxed-based matrix splitting method
- Relaxed-based Picard method
- Relaxed-based AOR method
- Relaxed-based SOR method
- Convergence