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has been cited by the following article:

• TITLE: Preconditioned Iterative Method for Regular Splitting

  AUTHORS: Toshiyuki Kohno

  KEYWORDS: Iterative Method, Splitting, Preconditioner, M-Matrix

  JOURNAL NAME: Advances in Pure Mathematics, Vol.7 No.2, February 9, 2017

  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.