Best Rational Approximation and Strict Quasi-Convexity

Date

1971

Authors

Barrodale, I

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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.

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Citation

Barrodale, I. (1971). Best Rational Approximation and Strict Quasi-Convexity. MRC Technical Summary Report #1157.