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Accelerated Relaxation Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

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Abstract

For solving large sparse linear complementarity problems effectively, by utilizing the parametric method, the acceleration strategy and the relaxation technique to the modulus-based matrix splitting (MMS) iteration method, we develop the accelerated relaxation MMS (ARMMS) iteration method, which generalizes the generalized accelerated MMS (GAMMS) and the relaxation MMS (RMMS) ones proposed recently. Meanwhile, it is proved that the ARMMS iteration method is convergent under proper restrictions when the system matrix is a positive definite matrix or an \(H_{+}\)-matrix. In addition, we also study the convergence properties of the ARM accelerated overrelaxation (ARMAOR) method. Numerical experiments show that the proposed iteration method is efficient, and it outperforms some existing ones with suitable choice of the parameter and matrix splitting.

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Acknowledgements

We would like to express our sincere thanks to the editor and the anonymous reviewer for their valuable suggestions and constructive comments which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. Faculty of Science, Guangxi University for Nationalities, Nanning, 530006, People’s Republic of China

    Zheng-Ge Huang

  2. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Jing-Jing Cui

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  1. Zheng-Ge Huang
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Correspondence to Zheng-Ge Huang.

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Communicated by Theodore E. Simos.

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This work was supported by the National Science Foundation (No. 11901123), the Guangxi Natural Science Foundation (No. 2018JJB110062) and the Xiangsihu Young Scholars Innovative Research Team of Guangxi University for Nationalities (No. 2019RSCXSHQN03).

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Huang, ZG., Cui, JJ. Accelerated Relaxation Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems. Bull. Malays. Math. Sci. Soc. 44, 2175–2213 (2021). https://doi.org/10.1007/s40840-020-01049-9

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  • DOI: https://doi.org/10.1007/s40840-020-01049-9

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