A formal study of Bernstein coefficients and polynomials

Yves Bertot 1 Frédérique Guilhot 1 Assia Mahboubi 2, 3
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
2 TYPICAL - Types, Logic and computing
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
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.
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Yves Bertot, Frédérique Guilhot, Assia Mahboubi. A formal study of Bernstein coefficients and polynomials. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2011, 21 (04), pp.731-761. ⟨10.1017/S0960129511000090⟩. ⟨inria-00503017v2⟩

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