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Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems

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  • Zhang, Yongxiong
  • Zheng, Hua
  • Lu, Xiaoping
  • Vong, Seakweng

Abstract

In this work, by applying the synchronous multisplitting technique to the non-auxiliary variable modulus equation of the vertical linear complementarity problems, a new parallel method is constructed, which can generalize the existing modulus-based matrix splitting iteration method. The convergence conditions of the proposed method are discussed in the cases of more than two system matrices, and the existing results are improved. Numerical examples under OpenACC framework show that the proposed method can solve the large sparse vertical linear complementarity problems efficiently with high parallel efficiency.

Suggested Citation

  • Zhang, Yongxiong & Zheng, Hua & Lu, Xiaoping & Vong, Seakweng, 2023. "Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004174
    DOI: 10.1016/j.amc.2023.128248
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    References listed on IDEAS

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    1. Cuiyu Liu & Chenliang Li, 2016. "Synchronous and Asynchronous Multisplitting Iteration Schemes for Solving Mixed Linear Complementarity Problems with H-Matrices," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 169-185, October.
    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. 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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