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The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

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Abstract

In this paper, by means of constructing the linear complementarity problems into the corresponding absolute value equation, we raise an iteration method, called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method, for solving the linear complementarity problems whose coefficient matrix in \(\mathbb {R}^{n\times n}\) is large sparse and positive definite. From the convergence analysis, it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions. Numerical examples demonstrate that the presented method precede to other methods in practical implementation.

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, China

    Lu Jia, Xiang Wang & Xiao-Yong Xiao

  2. Numerical Simulation and High-Performance Computing Laboratory, Nanchang University, Nanchang, 330031, China

    Xiang Wang

Authors
  1. Lu Jia
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  2. Xiang Wang
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  3. Xiao-Yong Xiao
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Correspondence to Xiang Wang.

Additional information

This work is supported by the National Natural Science Foundation of China with No. 11461046, the Natural Science Foundation of Jiangxi Province of China with Nos. 20181ACB20001 and 20161ACB21005.

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Jia, L., Wang, X. & Xiao, XY. The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices. Commun. Appl. Math. Comput. 3, 109–122 (2021). https://doi.org/10.1007/s42967-019-00038-5

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  • DOI: https://doi.org/10.1007/s42967-019-00038-5

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