Certificates of positivity in the simplicial Bernstein basis.

Richard Leroy (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study in the paper the positivity of real multivariate polynomials over a non-degenerate simplex V. We aim at obtaining certificates of positivity, {\it i.e.} algebraic identities certifying the positivity of a given polynomial on V, thus generalizing the work in \cite{BCR}. In order to do so, we use the Bernstein polynomials, which are more suitable than the usual monomial basis.

Mots clés: Bernstein basis : certificates of positivity

Domaines: Calcul formel [cs.SC]

Richard Leroy. Certificates of positivity in the simplicial Bernstein basis.. 2009. ⟨hal-00589945⟩