Preconditioned Iterative Method for Regular Splitting  

作　　者：Toshiyuki Kohno 

机构地区：[1]Department of Information Science, Okayama University of Science, Okayama, Japan

出　　处：《Advances in Pure Mathematics》2017年第2期180-187,共8页理论数学进展（英文）

摘　　要：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.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.

关 键 词：ITERATIVE METHOD SPLITTING PRECONDITIONER M-MATRIX 

分 类 号：O1[理学—数学]