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SOR-like iteration method for solving absolute value equations

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  • Ke, Yi-Fen
  • Ma, Chang-Feng

Abstract

In this paper, we propose an SOR-like iteration method for solving the absolute value equation (AVE), which is obtained by reformulating equivalently the AVE as a two-by-two block nonlinear equation. The convergence results of the proposed iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the SOR-like iteration method.

Suggested Citation

  • Ke, Yi-Fen & Ma, Chang-Feng, 2017. "SOR-like iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 195-202.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:195-202
    DOI: 10.1016/j.amc.2017.05.035
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    References listed on IDEAS

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    1. Louis Caccetta & Biao Qu & Guanglu Zhou, 2011. "A globally and quadratically convergent method for absolute value equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 45-58, January.
    2. J. Y. Bello Cruz & O. P. Ferreira & L. F. Prudente, 2016. "On the global convergence of the inexact semi-smooth Newton method for absolute value equation," Computational Optimization and Applications, Springer, vol. 65(1), pages 93-108, September.
    3. Edalatpour, Vahid & Hezari, Davod & Khojasteh Salkuyeh, Davod, 2017. "A generalization of the Gauss–Seidel iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 156-167.
    4. Moosaei, H. & Ketabchi, S. & Noor, M.A. & Iqbal, J. & Hooshyarbakhsh, V., 2015. "Some techniques for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 696-705.
    5. Zhang, Jian-Jun, 2015. "The relaxed nonlinear PHSS-like iteration method for absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 266-274.
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    Cited by:

    1. Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.

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