Numerical Analysis/Mathematical Analysis
Chebyshevian splines: interpolation and blossoms
Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 65-70.

We state and discuss a theorem which links the existence of blossoms in a spline space (with sections in different Extended Chebyshev spaces and with connection matrices which are not necessarily totally positive) with the possibility of Hermite interpolation in its derivative space under Schoenberg–Whitney conditions.

Cette note établit un lien fondamental entre existence de floraisons dans un espace de splines (à sections dans différents espaces de Chebyshev généralisés et avec matrices de connexion non nécessairement totalement positives) et possibilité d'interpoler au sens d'Hermite sous conditions de Schoenberg–Whitney.

Published online:
DOI: 10.1016/j.crma.2006.11.021
Kayumov, Alexander 1; Mazure, Marie-Laurence 2

1 Function Approximation Theory Department, Institute of Mathematics and Mechanics, 16, Sofia Kovalevskaya st., 620219 Ekaterinburg GSP-384, Russia
2 Laboratoire de modélisation et calcul (LMC-IMAG), université Joseph-Fourier, BP 53, 38041 Grenoble cedex 9, France
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Kayumov, Alexander; Mazure, Marie-Laurence. Chebyshevian splines: interpolation and blossoms. Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 65-70. doi : 10.1016/j.crma.2006.11.021.

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