Author(s)

Toshiyuki Kohno

Department of Information Science, Okayama University of Science, Okayama, Japan.

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.

Iterative Method, Splitting, Preconditioner, M-Matrix

Kohno, T. (2017) Preconditioned Iterative Method for Regular Splitting. Advances in Pure Mathematics, 7, 180-187. doi: 10.4236/apm.2017.72009.