IJPAM: Volume 65, No. 2 (2010)

A NOTE ON LOCATION AND ALGORITHMS
FOR FIXED POINTS

S. Shellman$^1$, K. Sikorski$^2$
$^{1,2}$50S. Central Campus Dr.
School of Computing
University of Utah
Salt Lake City, UT 84112, USA
$^1$e-mail: spenshel@yahoo.com
$^2$e-mail: sikorski@cs.utah.edu


Abstract.We present a constructive lemma on location of fixed points that we believe will make possible the design of nearly optimal $O(d\log\frac{1}{\epsilon})$ cost algorithms for computing $\epsilon$-residual approximations to the fixed points of $d$-dimensional nonexpansive mappings with respect to the infinity norm. This lemma is an extension of a two-dimensional result that we presented in [#!key-1!#].

Received: May 12, 2010

AMS Subject Classification: 65H10, 37C25

Key Words and Phrases: fixed points, algorithms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 2