InforLorV4, Hal, Curation, bibRecord, 001233

Bernstein's basis and real root isolation

Identifieur interne : 001233 ( Hal/Curation ); précédent : 001232; suivant : 001234

Bernstein's basis and real root isolation

Auteurs : Bernard Mourrain [France] ; Fabrice Rouillier [France] ; Marie-Françoise Roy

Source :

RBID : Hal:inria-00071434

Abstract

The Bernstein basis is widely used in Computer Aided Design. We explain how, combined with Descartes's rule, the Bernstein basis, provides as well an efficient method for real root isolation, using De Casteljau's algorithm, and make the link with more classical methods. Most of the content of the paper can be found in previous authors' articles. However, we present a new improved method for isolating real roots.

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https://hal.inria.fr/inria-00071434

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Le document en format XML

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<front><div type="abstract" xml:lang="en">The Bernstein basis is widely used in Computer Aided Design. We explain how, combined with Descartes's rule, the Bernstein basis, provides as well an efficient method for real root isolation, using De Casteljau's algorithm, and make the link with more classical methods. Most of the content of the paper can be found in previous authors' articles. However, we present a new improved method for isolating real roots.</div>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">Bernstein's basis and real root isolation</title>
<author role="aut"><persName><forename type="first">Bernard</forename>
<surname>Mourrain</surname>
</persName>
<email>mourrain@sophia.inria.fr</email>
<idno type="idHal">bernard-mourrain</idno>
<idno type="halAuthorId">79288</idno>
<idno type="arXiv">http://arxiv.org/a/mourrain</idno>
<affiliation ref="#struct-2461"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Fabrice</forename>
<surname>Rouillier</surname>
</persName>
<email>Fabrice.Rouillier@inria.fr</email>
<idno type="idHal">fabrice-rouillier</idno>
<idno type="halAuthorId">74826</idno>
<idno type="arXiv">http://arxiv.org/a/fabricerouillier</idno>
<affiliation ref="#struct-2364"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Marie-Françoise</forename>
<surname>Roy</surname>
</persName>
<idno type="halAuthorId">99314</idno>
<orgName ref="#struct-364174"></orgName>
</author>
</analytic>
<monogr><idno type="reportNumber">RR-5149</idno>
<imprint><date type="datePub">2004</date>
</imprint>
<authority type="institution">INRIA</authority>
</monogr>
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<profileDesc><langUsage><language ident="en">English</language>
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<textClass><keywords scheme="author"><term xml:lang="ro">COMPUTER ALGEBRA</term>
<term xml:lang="ro">UNIVARIATE POLYNOMIALS</term>
<term xml:lang="ro">REAL ROOTS</term>
</keywords>
<classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode>
<classCode scheme="halTypology" n="REPORT">Reports</classCode>
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<abstract xml:lang="en">The Bernstein basis is widely used in Computer Aided Design. We explain how, combined with Descartes's rule, the Bernstein basis, provides as well an efficient method for real root isolation, using De Casteljau's algorithm, and make the link with more classical methods. Most of the content of the paper can be found in previous authors' articles. However, we present a new improved method for isolating real roots.</abstract>
</profileDesc>
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Bernstein's basis and real root isolation

Bernstein's basis and real root isolation

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