A Simple Reordering Technique for Expanding the Convergence Radius of First Order Iterative Techniques

Andrew J. Hughes-Hallett
University of Strathclyde and CEPR

Laura Piscitelli
University of Strathclyde
Laura.Piscitelli@ccsun.strath.ac.uk

Abstract

This paper contains a new convergence theorem for Gauss-Seidel (SOR) iterations in the general case. It shows how to reorder equations to improve the speed of convergence of those iterations and, more importantly, their radius of convergence. It is not generally optimal to minimize the number or size of the above diagonal elements in a non-recursive system.