On the Optimality of Piecewise Linear Max-norm Enclosures based on Slefes
نویسنده
چکیده
Subdividable linear efficient function enclosures (Slefes) provide, at low cost, a piecewise linear pair of upper and lower bounds f, f, that sandwich a function f on a given interval: f ≥ f ≥ f. In practice, these bounds are observed to be very tight. This paper addresses the question just how close to optimal, in the max-norm, the slefe construction actually is. Specifically, we compare the width f−f of the slefe to the narrowest possible piecewise linear enclosure of f when f is a univariate cubic polynomial. §
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