Optimum Accelerated Overrelaxation (AOR) Method for Systems with Positive Definite Coefficient Matrix

Abstract

Given a linear system with a Hermitian positive definite coefficient matrix A, a splitting of it of Varga’s type [18] is considered and the corresponding generalized accelerated overrelaxation (AOR) scheme is formed. Under certain assumptions concerning one of the components of A and the convergence domains of the two parameters of the AOR method, an analysis analogous to that by Varga enables one to determine optimum values for the parameters involved. As both theory and numerical examples show, the optimum AOR method obtained in this way is faster than the corresponding SOR one.