The extrapolated gauss-seidel methods and generally consistently ordered matrices

Abstract

In this paper we investigate the convergence properties of the Extrapolated Gauss-Seidel 1 and 2 (EGS1 and EGS2) methods and the choice of their optimum factors on the basis of Generally Consistently Ordered (q r) matrices as defined by Verner and Bernal. It is shown how our results extend and correct some results in the literature.

Keywords:

• Jacobi iterative method
• Gauss-Seidel (GS) method
• Extrapolated Gauss-Seidel 1 and 2 (EGS1 and EGS2) methods
• Successive Overrelaxation (SOR) method
• Generally Consistently Ordered (q r) (GCO(q r)) matrices
• Spectral Radius and Asymptotic Rate of Convergence

C.R. Categories:

• G.7.3
• G.1.8