A note on two fixed point problems

Authors:
Ch. Boonyasiriwat;K. Sikorski;Ch. Xiong
Affiliations:
School of Computing, University of Utah, Salt Lake City, UT 84112, USA;School of Computing, University of Utah, Salt Lake City, UT 84112, USA;Department of Chemistry, University of Utah, Salt Lake City, UT 84112, USA
Venue:
Journal of Complexity
Year:
2007

Citing 13
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Abstract

We extend the applicability of the Exterior Ellipsoid Algorithm for approximating n-dimensional fixed points of directionally nonexpanding functions. Such functions model many practical problems that cannot be formulated in the smaller class of globally nonexpanding functions. The upper bound 2n^2ln(2/@?) on the number of function evaluations for finding @?-residual approximations to the fixed points remains the same for the larger class. We also present a modified version of a hybrid bisection-secant method for efficient approximation of univariate fixed point problems in combustion chemistry.