Post-processing of Gauss-Seidel iterations

We examine a simple post-processing technique when solving the system of n linear algebraic equations Ax = b with a nonsingular matrix using the classical iterative methods such as the Gauss-Seidel method. We prove that this technique accelerates the convergence of iterations. Its efficiency is demonstrated on a system arising from a finite element approximation of a second order elliptic boundary value problem. Copyright (C) 1999 John Wiley & Sons, Ltd.