THREE OPTIMIZATION MODELS FOR MULTISPLITTING PRECONDITIONER

Liang Wei () and Chuan-Long Wang ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2013, vol. 30, issue 03, 1-14

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.

Keywords: Optimal weighting parameters; multisplitting; preconditioner; minimize models; convergence (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S0217595913400071

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