Best Rational Approximation and Strict Quasi-Convexity
Date
1971
Authors
Barrodale, I
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
If a continuous function is strictly quasi-convex on a convex set $\Gamma $, then every local minimum of the function must be a global minimum. Furthermore, every local maximum of the function on the interior of $\Gamma $ must also be a global minimum. Here, we prove that any minimax rational approximation problem defines a strictly quasi-convex function with the property that a best approximation (if one exists) is a minimum of that function. The same result is not true in general for best rational approximation in other norms.
Description
Keywords
Citation
Barrodale, I. (1971). Best Rational Approximation and Strict Quasi-Convexity. MRC Technical Summary Report #1157.