An error bound for the modified successive overrelaxation method

In this paper we consider the modified successive overrelaxation(MSOR)methodto appropriate the solution of the linear system D^-1/2 Ax =D^-1/2b, where A is a symmetric, positive definite and consistentlyordered matrix and D is a diagonal matrix with the diagonalidentical to that of A. The main purpose of this paper is to obtain some theoreticalresults, namely a bound for the norm of _n = v –v_n in termsof the norms _n –v_n-1, _n+1 –v_n and their inner product,where v =D^-1/2 x and v_n is the nth iteration vector, obtainedusing the (MSOR)method.