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Modified iterative method for augmented system

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Abstract

The successive overrelaxation-like (SOR-like) method with the real parameters ω is considered for solving the augmented system. The new method is called the modified SOR-like (MSOR-like) method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like (Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel & Scientific Computations, 7(4), 453–462 (1999)) and the modified symmetric SOR-like (MSSOR-like) methods (Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228(4), 424–433 (2009)).

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Shenyang, 110004, P.R. China

    Xin-hui Shao  (邵新慧), Cui Ji  (季 翠), Hai-long Shen  (沈海龙) & Chang-jun Li  (李长军)

Authors
  1. Xin-hui Shao  (邵新慧)
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  2. Cui Ji  (季 翠)
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  3. Hai-long Shen  (沈海龙)
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  4. Chang-jun Li  (李长军)
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Corresponding author

Correspondence to Hai-long Shen  (沈海龙).

Additional information

Project supported by the National Natural Science Foundation of China (No. 10771031) and the Fundamental Research Funds for Central Universities (No. 090405013)

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Shao, Xh., Ji, C., Shen, Hl. et al. Modified iterative method for augmented system. Appl. Math. Mech.-Engl. Ed. 35, 503–514 (2014). https://doi.org/10.1007/s10483-014-1808-8

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  • DOI: https://doi.org/10.1007/s10483-014-1808-8

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Chinese Library Classification

2010 Mathematics Subject Classification

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