REFINEMENT OF PRECONDITIONED OVERRELAXATION ALGORITHM FOR SOLUTION OF THE LINEAR ALGEBRAIC SYSTEM Ax=b

Abstract

In this paper, a refinement of preconditioned successive overrelaxation method for solving the linear system  is considered. The coefficient matrix  is a nonsingular real matrix,  and  is the vector of unknowns. Based on the usual splitting of the coefficient matrix  as , the linear system is expressed as  or ; where ,  and . This system is further preconditioned with a preconditioner of the type  as   or . A refinement of the resulting preconditioned successive overrelaxation (SOR) method is performed. Convergence of the resulting refinement of preconditioned SOR iteration is established and numerical experiments undertaken to demonstrate the effectiveness and efficiency of the method. Results comparison revealed that the refinement of SOR method converges faster than the preconditioned as well as the classical SOR method.