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Convergence analysis of projected SOR iteration method for a class of vertical linear complementarity problems

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Abstract

Based on the ideas of the projected matrix splitting technique and the well-known successive overrelaxation (SOR) iteration method, a projected SOR (PSOR) iteration method is studied in this paper for solving a class of vertical linear complementarity problems, where the system matrix is a vertical block matrix of several square sub-blocks with positive diagonal elements. Convergence analyses of the PSOR iteration method are carefully studied when the square sub-blocks and their row-representative matrices are strictly diagonally dominant, irreducibly diagonally dominant and \(H_{+}\)-matrices, respectively. At last, two numerical examples are presented. Numerical results indicate that the PSOR method performs much better than some recent proposed projected splitting methods.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11771225), the QingLan Project of Jiangsu Province (No. 06210057), and the Science and Technology Project of Nantong City (No. JC2021198).

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Authors and Affiliations

  1. School of Transportation and Civil Engineering, Nantong University, Nantong, 226019, People’s Republic of China

    Yang Cao & Qin-Qin Shen

  2. School of Sciences, Nantong University, Nantong, 226019, People’s Republic of China

    Yang Cao & Geng-Chen Yang

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  1. Yang Cao
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  2. Geng-Chen Yang
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Correspondence to Qin-Qin Shen.

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Communicated by Zhong-Zhi Bai.

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Cao, Y., Yang, GC. & Shen, QQ. Convergence analysis of projected SOR iteration method for a class of vertical linear complementarity problems. Comp. Appl. Math. 42, 191 (2023). https://doi.org/10.1007/s40314-023-02334-6

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