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Preconditioned Iterative Method for Regular Splitting
Department of Information Science, Okayama University of Science, Okayama, Japan
- 1 Department of Information Science, Okayama University of Science, Okayama, Japan
Advances in Pure Mathematics·Volume 07 (2017)·Pages 180–187·Published 7 February 2017·DOI10.4236/apm.2017.72009
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Abstract
Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.
KeywordsIterative MethodSplittingPreconditionerM-Matrix
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