Refinement of Generalized Accelerated Over Relaxation Method for Solving System of Linear Equations Based on the Nekrassov-Mehmke1-Method

Abstract

In this paper, refinement of generalized accelerated over relaxation (RGAOR) iterative method is presented based on the Nekrassov-Mehmke 1- method (NM1) procedure for solving system of linear equations of the form , where is a nonsingular real matrix of order , is a given dimensional real vector. The coefficient matrix is split as in , where is a banded matrix of band width and and are strictly lower and strictly upper triangular parts of the matrix respectively. The finding shows that the iterative matrix of the new method is the square of generalized accelerated successive over relaxation iterative matrix. The convergence of the new method is studied and few numerical examples are considered to show the efficiency of the proposed methods. As compared to generalized accelerated successive over relaxation (SOR2GNM1, SOR1GNM1), the results reveal that the present method (RSOR1GNM1, RSOR2GNM1) converges faster and its error at any predefined error of tolerance is less than the other methods used for comparison.

Keywords: Convergence, M-matrix, Nekrassov-Mehmke 1- method, Refinement of Generalized accelerated over relaxation