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A class of modified modulus-based synchronous multisplitting iteration methods for linear complementarity problems

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Abstract

In this paper, we present modified modulus-based synchronous multisplitting iteration methods based on multisplittings of the system matrix for solving the large sparse linear complementarity problems. The proposed methods extend the existing modulus-based synchronous multisplitting iteration methods to a more general case. We establish the convergence theory of these modified modulus-based synchronous multisplitting iteration methods when the system matrix is an H+-matrix. In particular, we investigate the optimal choice of the parameter matrices in theory. Numerical results confirm that the new iteration methods have higher parallel computational efficiency than the existing modulus-based synchronous multisplitting iteration methods. The proposed methods are applied in reconstruction of two-dimensional image data and show the efficiency.

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Acknowledgments

The authors are very grateful to the referees for their constructive suggestions and helpful comments. Sincere thanks to Prof. Wen Li from South China Normal University for his many helpful suggestions in mathematics.

Funding

The work was supported by the Jiangsu Provincial Natural Science Foundation of Jiangsu Province of China under Grant No. BK20181405 and the National Natural Science Foundation of China under Grant Nos. 11971243, U1533202, U1811464, 11571124, 11671158, 11401305, 11971354, 61573181 and Civil Aviation Science and Technology Project under Grant No. 20150218.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of information Science and Technology, Nanjing, China

    Weiwei Xu

  2. College of Engineering, Nanjing Agricultural University, Nanjing, China

    Lei Zhu

  3. School of Mathematical Sciences, South China Normal University, Guangzhou, China

    Xiaofei Peng

  4. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Hao Liu

  5. School of Mathematical Sciences, Tongji University, Shanghai, China

    Junfeng Yin

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  1. Weiwei Xu
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  2. Lei Zhu
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  3. Xiaofei Peng
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  4. Hao Liu
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  5. Junfeng Yin
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Correspondence to Xiaofei Peng.

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Xu, W., Zhu, L., Peng, X. et al. A class of modified modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numer Algor 85, 1–21 (2020). https://doi.org/10.1007/s11075-019-00799-3

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  • DOI: https://doi.org/10.1007/s11075-019-00799-3

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