[An effective bound on the gap between the control polytope and the graph of a real polynomial on a simplex]
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.
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.
Accepted:
Published online:
Richard Leroy 1
@article{CRMATH_2009__347_23-24_1331_0, author = {Richard Leroy}, title = {Une borne effective sur l'\'ecart entre le polytope de contr\^ole et le graphe d'un polyn\^ome r\'eel sur un simplexe}, journal = {Comptes Rendus. Math\'ematique}, pages = {1331--1336}, publisher = {Elsevier}, volume = {347}, number = {23-24}, year = {2009}, doi = {10.1016/j.crma.2009.10.011}, language = {fr}, }
TY - JOUR AU - Richard Leroy TI - Une borne effective sur l'écart entre le polytope de contrôle et le graphe d'un polynôme réel sur un simplexe JO - Comptes Rendus. Mathématique PY - 2009 SP - 1331 EP - 1336 VL - 347 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2009.10.011 LA - fr ID - CRMATH_2009__347_23-24_1331_0 ER -
Richard Leroy. Une borne effective sur l'écart entre le polytope de contrôle et le graphe d'un polynôme réel sur un simplexe. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1331-1336. doi : 10.1016/j.crma.2009.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.011/
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