On the convergence of parallel nonstationary multisplitting iteration methods

Abstract

The convergence properties of a variant of the parallel chaotic multisplitting iteration method, called the nonstationary multisplitting iteration method, for solving large sparse systems of linear equations are further discussed when the coefficient matrix is an H-matrix or a positive definite matrix, respectively. Moreover, when the coefficient matrix is a monotone matrix, the monotone convergence theory and the monotone comparison theorem about this method are established. This directly leads to several novel sufficient conditions for guaranteeing the convergence of this parallel nonstationary multisplitting iteration method.