Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions

Titi, Jihad; Garloff, Jürgen

Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions

Dateien

Titi_0-410198.pdfGröße: 345.21 KBDownloads: 559

Datum

2017

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

Zusammenfassung

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Multivariate polynomial, multivariate rational function, Bernstein coefficient, tensorial Bernstein form, simplicial Bernstein form, range enclosure

Zitieren

ISO 690

TITI, Jihad, Jürgen GARLOFF, 2017. Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions

BibTex

@techreport{Titi2017Deter-39178,
  year={2017},
  series={Konstanzer Schriften in Mathematik},
  title={Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions},
  number={361},
  author={Titi, Jihad and Garloff, Jürgen}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39178">
    <dcterms:issued>2017</dcterms:issued>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-06-08T13:55:57Z</dcterms:available>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:language>eng</dc:language>
    <dc:creator>Titi, Jihad</dc:creator>
    <dcterms:title>Fast Determination of the Tensorial and Simplicial Bernstein Forms of Multivariate Polynomials and Rational Functions</dcterms:title>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/39178/3/Titi_0-410198.pdf"/>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:creator>Garloff, Jürgen</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-06-08T13:55:57Z</dc:date>
    <dc:contributor>Titi, Jihad</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Garloff, Jürgen</dc:contributor>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/39178"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/39178/3/Titi_0-410198.pdf"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja