Isolation of Real Roots and Computation of the Topological Degree

Bernard Mourrain 1 Michael N. Vrahatis 1 Jean-Claude Yakoubsohn 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this work, the isolation of real rootsbased on Bernstein polynomials, and the computation of the topological degree in two dimensions are considered and their complexity is analyzed. In particular, we apply Stenger's degree computational method by splitting properly the boundary of the given region to obtain a sequence of subintervals along the boundary that forms a sufficien- t refinement. To this end, we properly approximate the function using univariate polynomials. Then we isolate each one of the zeros of these polynomials on the boundary of the given region in various subintervals so that these subintervals form a sufficiently refined boundary.
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https://hal.inria.fr/inria-00072287
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Submitted on : Tuesday, May 23, 2006 - 8:18:49 PM
Last modification on : Thursday, January 11, 2018 - 3:57:42 PM
Long-term archiving on : Sunday, April 4, 2010 - 11:02:14 PM

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  • HAL Id : inria-00072287, version 1

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Bernard Mourrain, Michael N. Vrahatis, Jean-Claude Yakoubsohn. Isolation of Real Roots and Computation of the Topological Degree. [Research Report] RR-4300, INRIA. 2001. ⟨inria-00072287⟩

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