How to improve on the convergence rates of a first order scheme

Abstract

In this paper a one-parametric stationary method, known as extrapolation, for improving the convergence rates of a first order iterative scheme, for the numerical solution of the linear system Ax = b, is studied. First an analytical determination of good-optimum values of the extrapolation parameter, under some simple assumptions, is made. Then a geometrical interpretation of the method and the optimum results are presented. Finally some applications and numerical examples are given which support the theory developed from both the analytical and geometrical point of view.