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Convergence of the Simplicial Rational Bernstein Form

  • Bernstein polynomials on a simplex V are considered. The expansion of a given polynomial p into these polynomials provides bounds for range of p over V. Bounds for the range of a rational function over V can easily be obtained from the Bernstein expansions of the numerator and denominator polynomials of this function. In this paper it is shown that these bounds converge monotonically and linearly to the range of the rational function if the degree of the Bernstein expansion is elevated. If V is subdivided then the convergence is quadratic with respect to the maximum of the diameters of the subsimplices.

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Author:Jihad TitiORCiD, Tareq Hamadneh, Jürgen GarloffORCiDGND
Parent Title (English):Modelling, Computation and Optimization in Information Systems and Management Sciences Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 359)
Document Type:Article
Year of Publication:2015
Identifier:Im Katalog der Hochschule Konstanz ansehen
Release Date:2017/07/18
Tag:Bernstein polynomial; simplex; range bounds; rational function; degree elevation
First Page:433
Last Page:441
Open Access?:Ja
Licence (German):License LogoLizenz nach Vereinbarung