HAL - INRIA :: [inria-00503017, version 2] A formal study of Bernstein coefficients and polynomials

inria-00503017, version 2

A formal study of Bernstein coefficients and polynomials

Yves Bertot ( Author to contact preferably ) ^1, 2, Frédérique Guilhot () ¹, Assia Mahboubi () ^2, 3, 4

Mathematical Structures in Computer Science 21, 04 (2011) 731-761

Abstract: Bernstein coefficients provide a discrete approximation of the behavior of a polynomial inside an interval. This can be used for example to isolate real roots of polynomials. We prove a criterion for the existence of a single root in an interval and the correctness of the de Casteljau algorithm to compute efficiently Bernstein coefficients.

1: MARELLE (INRIA Sophia Antipolis)
INRIA
2: Microsoft Research - Inria Joint Centre (MSR - INRIA)
INRIA – Microsoft – Microsoft Research Laboratory Cambridge
3: TypiCal (INRIA Saclay - Ile de France)
INRIA – CNRS : UMR – Polytechnique - X
4: Laboratoire d'informatique de l'école polytechnique (LIX)
CNRS : UMR7161 – Polytechnique - X

inria-00503017, version 2
http://hal.inria.fr/inria-00503017
oai:hal.inria.fr:inria-00503017
From: Assia Mahboubi <>
Submitted on: Wednesday, 22 September 2010 12:27:26
Updated on: Saturday, 2 July 2011 15:10:35

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