• search hit 1 of 4
Back to Result List

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.

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Jihad TitiORCiD, Tareq Hamadneh, Jürgen GarloffORCiDGND
URL:http://www-home.htwg-konstanz.de/%7Egarloff/Paper95_MCO2015_Titi_Hamadneh_Garloff(1).pdf
DOI:https://doi.org/10.1007/978-3-319-18161-5
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
Language:English
Year of Publication:2015
Opac ID:Im Katalog der Hochschule Konstanz ansehen
Release Date:2017/07/18
Tag:Bernstein polynomial; degree elevation; range bounds; rational function; simplex
First Page:433
Last Page:441
Open Access?:Ja
Licence (German):License LogoLizenz nach Vereinbarung