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A preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problem

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  • Dai, Ping-Fan
  • Li, Jicheng
  • Bai, Jianchao
  • Qiu, Jinming

Abstract

In this paper, a preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problems associated with an M-matrix is proposed. The convergence analysis of the presented method is given. In particular, we provide a comparison theorem between preconditioned two-step modulus-based Gauss–Seidel (PTMGS) iteration method and two-step modulus-based Gauss–Seidel (TMGS) iteration method, which shows that PTMGS method improves the convergence rate of original TMGS method for linear complementarity problem. Numerical tested examples are used to illustrate the theoretical analysis.

Suggested Citation

  • Dai, Ping-Fan & Li, Jicheng & Bai, Jianchao & Qiu, Jinming, 2019. "A preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 542-551.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:542-551
    DOI: 10.1016/j.amc.2018.12.012
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    References listed on IDEAS

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    1. Zhong-Zhi Bai, 2001. "Modified Block SSOR Preconditioners for Symmetric Positive Definite Linear Systems," Annals of Operations Research, Springer, vol. 103(1), pages 263-282, March.
    2. 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. Zhang, Li-Li, 2021. "A modulus-based multigrid method for nonlinear complementarity problems with application to free boundary problems with nonlinear source terms," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    2. Ali, Rashid & Akgul, Ali, 2024. "A new matrix splitting generalized iteration method for linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 464(C).

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