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On convergence of the modulus-based matrix splitting iteration method for horizontal linear complementarity problems of H+-matrices

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  • Zheng, Hua
  • Vong, Seakweng

Abstract

Horizontal linear complementarity problem has wide applications, such as in mechanical and electrical engineering, structural mechanics, piecewise linear system, telecommunication systems and so on. In this paper, we focus on the convergence conditions of the modulus-based matrix splitting iteration method proposed recently for solving horizontal linear complementarity problems. By the proposed theorems, the assumptions on the matrix splitting and the system matrices are weakened, and the convergence domain is enlarged. Numerical examples are presented to show the improvement.

Suggested Citation

  • Zheng, Hua & Vong, Seakweng, 2020. "On convergence of the modulus-based matrix splitting iteration method for horizontal linear complementarity problems of H+-matrices," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308823
    DOI: 10.1016/j.amc.2019.124890
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    1. B. C. Eaves & C. E. Lemke, 1981. "Equivalence of LCP and PLS," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 475-484, November.
    2. Xia, Zechen & Li, Chenliang, 2015. "Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 34-42.
    3. Yinyu Ye, 1993. "A Fully Polynomial-Time Approximation Algorithm for Computing a Stationary Point of the General Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 334-345, May.
    4. Francesco Mezzadri & Emanuele Galligani, 2019. "Splitting Methods for a Class of Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 500-517, February.
    5. H. Saberi Najafi & S. A. Edalatpanah, 2013. "On the Convergence Regions of Generalized Accelerated Overrelaxation Method for Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 859-866, March.
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    Cited by:

    1. Cuixia Li & Shiliang Wu, 2023. "An Improved Convergence Condition of the MMS Iteration Method for Horizontal LCP of H + -Matrices," Mathematics, MDPI, vol. 11(8), pages 1-6, April.
    2. Zhang, Yongxiong & Zheng, Hua & Vong, Seakweng & Lu, Xiaoping, 2023. "A two-step parallel iteration method for large sparse horizontal linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    3. Zheng, Hua & Vong, Seakweng, 2021. "On the modulus-based successive overrelaxation iteration method for horizontal linear complementarity problems arising from hydrodynamic lubrication," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    4. Mezzadri, Francesco & Galligani, Emanuele, 2020. "On the convergence of modulus-based matrix splitting methods for horizontal linear complementarity problems in hydrodynamic lubrication," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 226-242.

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