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A preconditioned general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems

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Abstract

In this paper, first we propose a general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems. In order to improve the computing efficiency, we further propose a preconditioned general modulus-based matrix splitting iteration method. We establish the convergence theorems when the coefficient matrices are (symmetric) positive definite matrices and H+-matrices, respectively. Numerical results show that the proposed preconditioned general modulus-based matrix splitting iteration method is superior than some existing methods and the general modulus-based matrix splitting iteration method.

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Funding

This work was supported by the National Natural Science Foundation of China (No. 11771193) the Fundamental Research Funds for the Central Universities, No.lzujbky-2022-05.

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  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Si-Wei Liao, Guo-Feng Zhang & Zhao-Zheng Liang

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  1. Si-Wei Liao
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  2. Guo-Feng Zhang
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  3. Zhao-Zheng Liang
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Correspondence to Guo-Feng Zhang.

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Liao, SW., Zhang, GF. & Liang, ZZ. A preconditioned general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems. Numer Algor 93, 919–947 (2023). https://doi.org/10.1007/s11075-022-01447-z

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