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Three Optimization Models For Multisplitting Preconditioner

Author

Listed:
  • LIANG WEI

    (Institution of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Shanxi Province, P. R. China)

  • CHUAN-LONG WANG

    (Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, Shanxi Province, P. R. China)

Abstract

In this paper, we use matrix multisplitting with weighting parameters as the preconditioner of A. The optimal weighting parameters are determined by the approaching theory, and the scale of approaching is defined by F-norm, 2-norm, and ∞-norm, respectively. Base on these three minimize models, three algorithms are presented and the convergence theories are established. Finally, numerical examples show that the preconditioner with the optimal weighting parameters, which are obtained from minimize F-norm and 2-norm models, can improve the condition number of A effectively. Besides, general weighting parameters are more effective than non-negative weighting parameters.

Suggested Citation

  • Liang Wei & Chuan-Long Wang, 2013. "Three Optimization Models For Multisplitting Preconditioner," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-14.
    • Handle: RePEc:wsi:apjorx:v:30:y:2013:i:03:n:s0217595913400071
    DOI: 10.1142/S0217595913400071
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