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Journal Articles Mathematical Structures in Computer Science Year : 2011

A formal study of Bernstein coefficients and polynomials

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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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Dates and versions

inria-00503017 , version 1 (16-07-2010)
inria-00503017 , version 2 (05-11-2014)

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Yves Bertot, Frédérique Guilhot, Assia Mahboubi. A formal study of Bernstein coefficients and polynomials. Mathematical Structures in Computer Science, 2011, 21 (04), pp.731-761. ⟨10.1017/S0960129511000090⟩. ⟨inria-00503017v2⟩
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