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More on matrix splitting modulus-based iterative methods for solving linear complementarity problem

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Abstract

In this article, we present a class of new modified modulus-based matrix spitting methods to process the large and sparse linear complementarity problem (LCP). Using two positive diagonal matrices, we formulate an implicit fixed-point equation that is equivalent to a LCP and an iterative method is presented to solve the LCP with a P-matrix based on a fixed-point equation. Also, we provide some sufficient convergence conditions for the proposed methods when the system matrix is an \(H_+\)-matrix. We provide two numerical examples to demonstrate the efficiency of the proposed methods.

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Acknowledgements

The author, Bharat Kumar, is thankful to the University Grants Commission (UGC), Government of India, under the SRF fellowship, Ref. No.: 1068/(CSIR-UGC NET DEC. 2017). The authors are grateful to the editor associated with this paper for their excellent suggestions. Also, the authors thank the anonymous referees who spent their precious time reviewing this paper. The authors would like to acknowledge their contribution, due to which there is a significant improvement in the paper.

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Authors and Affiliations

  1. Mathematics Discipline, PDPM-Indian Institute of Information Technology Design and Manufacturing, Dumna Road, Jabalpur, MP, 482005, India

    Bharat Kumar &  Deepmala

  2. Department of Mathematics, Jadavpur University, 188 Raja S.C. Mallick Rd, Jadavpur, WB, 700032, India

    A. Dutta

  3. SQC & OR Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, WB, 700108, India

    A. K. Das

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  1. Bharat Kumar
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Kumar, B., Deepmala, Dutta, A. et al. More on matrix splitting modulus-based iterative methods for solving linear complementarity problem. OPSEARCH 60, 1003–1020 (2023). https://doi.org/10.1007/s12597-023-00634-3

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