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Modified Picard-like Method for Solving Absolute Value Equations

Author

Listed:
  • Yuan Liang

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, China)

  • Chaoqian Li

    (School of Mathematics and Statistics, Yunnan University, Kunming 650504, China)

Abstract

We present a modified Picard-like method to solve absolute value equations by equivalently expressing the implicit fixed-point equation form of the absolute value equations as a two-by-two block nonlinear equation. This unifies some existing matrix splitting algorithms and improves the efficiency of the algorithm by introducing the parameter ω . For the choice of ω in the new method, we give a way to determine the quasi-optimal values. Numerical examples are given to show the feasibility of the proposed method. It is also shown that the new method is better than those proposed by Ke and Ma in 2017 and Dehghan and Shirilord in 2020.

Suggested Citation

  • Yuan Liang & Chaoqian Li, 2023. "Modified Picard-like Method for Solving Absolute Value Equations," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:848-:d:1060582
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    References listed on IDEAS

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    1. An Wang & Yang Cao & Jing-Xian Chen, 2019. "Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 216-230, April.
    2. Javed Iqbal & Muhammad Arif, 2013. "Symmetric SOR Method for Absolute Complementarity Problems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, September.
    3. Muhammad Aslam Noor & Javed Iqbal & Eisa Al-Said, 2012. "Residual Iterative Method for Solving Absolute Value Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, March.
    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. Muhammad Aslam Noor & Javed Iqbal & Khalida Inayat Noor & E. Al-Said, 2012. "Generalized AOR Method for Solving Absolute Complementarity Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, April.
    6. Saeed Ketabchi & Hossein Moosaei, 2012. "Minimum Norm Solution to the Absolute Value Equation in the Convex Case," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 1080-1087, September.
    7. 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.
    8. 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.
    9. Cui-Xia Li, 2016. "A Modified Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1055-1059, September.
    10. Shi-Liang Wu & Peng Guo, 2016. "On the Unique Solvability of the Absolute Value Equation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 705-712, May.
    11. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. Lei Shi & Javed Iqbal & Faiqa Riaz & Muhammad Arif, 2023. "Gauss Quadrature Method for System of Absolute Value Equations," Mathematics, MDPI, vol. 11(9), pages 1-8, April.

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