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Fast determination of the tensorial and simplicial Bernstein forms of multivariate polynomials and rational functions

  • Tests for speeding up the determination of the Bernstein enclosure of the range of a multivariate polynomial and a rational function over a box and a simplex are presented. In the polynomial case, this enclosure is the interval spanned by the minimum and the maximum of the Bernstein coefficients which are the coefficients of the polynomial with respect to the tensorial or simplicial Bernstein basis. The methods exploit monotonicity properties of the Bernstein coefficients of monomials as well as a recently developed matrix method for the computation of the Bernstein coefficients of a polynomial over a box.

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Metadaten
Author:Jihad TitiORCiD, Jürgen GarloffORCiDGND
URL:http://nbn-resolving.de/urn:nbn:de:bsz:352-0-410198
ISSN:1573-1340
Parent Title (English):Reliable Computing Journal
Document Type:Article
Language:English
Year of Publication:2017
Release Date:2019/05/17
Tag:Bernstein coefficient; Multivariate polynomial; Multivariate rational function; Simplicial Bernstein form; Tensorial Bernstein form
Issue:25
First Page:24
Last Page:37
Open Access?:Ja
Relevance:Peer reviewed Publikation entsprechend Liste der AG4