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The nonlinear lopsided PSS-like and HSS-like modulus-based matrix splitting iteration methods for horizontal linear complementarity problem

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Abstract

For solving horizontal linear complementarity problem (HLCP), we propose a nonlinear lopsided PSS-like modulus-based matrix splitting iteration method and a new nonlinear lopsided PSS-like modulus-based matrix splitting iteration method according to the characteristics of the HLCP. The proposed methods contain the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method and a new nonlinear lopsided HSS-like modulus-based matrix splitting iteration method. When the system matrices are positive definite matrices, we analyze the proposed methods in theory and prove the convergence of these methods. Numerical experiments in this paper demonstrate the effectiveness of the proposed methods.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 12171384).

Funding

This work was supported by National Natural Science Foundation of China (Grant No. 12171384).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Dan Wang & Jicheng Li

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  1. Dan Wang
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  2. Jicheng Li
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DW wrote the original manuscript and modified manuscript. JCL read this manuscript and gave suggestions.

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Correspondence to Jicheng Li.

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Wang, D., Li, J. The nonlinear lopsided PSS-like and HSS-like modulus-based matrix splitting iteration methods for horizontal linear complementarity problem. Comp. Appl. Math. 42, 299 (2023). https://doi.org/10.1007/s40314-023-02433-4

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  • DOI: https://doi.org/10.1007/s40314-023-02433-4

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