A MODIFIED SOR ITERATIVE SCHEME FOR SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS WITH M-MATRICES

Abstract

This present work concerns the theoretical and numerical investigation of a new combination preconditioner applied to the successive overrelaxation (SOR) method, in order to speed up its convergence for solving large sparse linear algebraic systems whose coefficient matrix is an L-matrix. The structures and properties of some lower triangular, upper triangular and combination preconditioners are studied, and a new combination preconditioner is proposed. The results of comparison theorems and numerical experiments revealed that the proposed preconditioned SOR scheme is the best one among all corresponding results, as it maintains faster convergence rate.