On the Convergence of Some Generalized Preconditioned Iterative Methods

Abstract

This paper generalizes the preconditioning techniques introduced by Evans [2] for the numerical solution of the linear system $Au = b$ and defines two extrapolated versions of the Gauss–Siedel method as well as an extrapolated version of the successive overrelaxation method. Finally, it establishes some convergence theorems for the considered iterative schemes when A has particular properties such as being consistently ordered, positive definite having weak diagonal dominance, etc...