Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 821928, 13 pages
doi:10.1155/2010/821928
Research Article

Nonexpansive Matrices with Applications to Solutions of Linear Systems by Fixed Point Iterations

Teck-Cheong Lim

Department of Mathematical Sciences, George Mason University, 4400, University Drive, Fairfax, VA 22030, USA

Received 28 August 2009; Accepted 19 October 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Teck-Cheong Lim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We characterize (i) matrices which are nonexpansive with respect to some matrix norms, and (ii) matrices whose average iterates approach zero or are bounded. Then we apply these results to iterative solutions of a system of linear equations.