Efficient Isolation of a Polynomial Real Roots
Identifieur interne : 009661 ( Main/Exploration ); précédent : 009660; suivant : 009662Efficient Isolation of a Polynomial Real Roots
Auteurs : Fabrice Rouillier [France] ; Paul Zimmermann [France]Source :
English descriptors
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Abstract
This paper gives new results for the isolation of real roots of a univariate polynomial using Descartes' rule of signs, following work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick. The first contribution is a generic algorithm which enables one to describe all the existing strategies in a unified framework. Using that framework, a new algorithm is presented, which is optimal in terms of memory usage, while doing no more computations than other algorithms based on Descartes' rule of signs. We show that these critical optimizations have important consequences by proposing a full efficient solution for isolating the real roots of zero-dimensional polynomial systems.
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Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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ISOLATION</term><term>UNIVARIATE POLYNOMIAL</term><term>USPENSKY'S ALGORITHM</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">This paper gives new results for the isolation of real roots of a univariate polynomial using Descartes' rule of signs, following work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick. The first contribution is a generic algorithm which enables one to describe all the existing strategies in a unified framework. Using that framework, a new algorithm is presented, which is optimal in terms of memory usage, while doing no more computations than other algorithms based on Descartes' rule of signs. We show that these critical optimizations have important consequences by proposing a full efficient solution for isolating the real roots of zero-dimensional polynomial systems.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Rouillier, Fabrice" sort="Rouillier, Fabrice" uniqKey="Rouillier F" first="Fabrice" last="Rouillier">Fabrice Rouillier</name></region><name sortKey="Zimmermann, Paul" sort="Zimmermann, Paul" uniqKey="Zimmermann P" first="Paul" last="Zimmermann">Paul Zimmermann</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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