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Comptes Rendus Mathématique
Volume 347, n° 23-24
pages 1331-1336 (décembre 2009)
Doi : 10.1016/j.crma.2009.10.011
Received : 19 February 2009 ;  accepted : 12 October 2009
Une borne effective sur l’écart entre le polytope de contrôle et le graphe d’un polynôme réel sur un simplexe
An effective bound on the gap between the control polytope and the graph of a real polynomial on a simplex
 

Richard Leroy
IRMAR, Université Rennes 1, 263, Mathematics, Bureau 634, avenue du General Leclerc, CS 74205, 35042 Rennes cedex, France 

Résumé

On établit dans cette Note une borne explicite sur l’écart entre le polytope de contrôle et le graphe du polynôme réel exprimé dans la base de Bernstein associée à un simplexe. Cette borne généralise les résultats connus en dimensions 1 et 2. Pour citer cet article : R. Leroy, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.
Abstract

We provide in this Note an explicit bound on the gap between the control polytope and the graph of a real polynomial, expressed in the simplicial Bernstein basis. This generalizes known results in dimensions 1 and 2. To cite this article: R. Leroy, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.


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