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Bernstein's basis and real root isolation

Bernard Mourrain 1 Fabrice Rouillier 2 Marie-Françoise Roy
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
2 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Submitted on : Tuesday, May 23, 2006 - 5:32:27 PM
Last modification on : Thursday, January 20, 2022 - 4:13:30 PM
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  • HAL Id : inria-00071434, version 1


Bernard Mourrain, Fabrice Rouillier, Marie-Françoise Roy. Bernstein's basis and real root isolation. [Research Report] RR-5149, INRIA. 2004. ⟨inria-00071434⟩



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