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ESAIM: Proc., 2007, Vol. 20, pp. 63-71
DOI: 10.1051/proc:072006
data fitting by vector (V,f)-reproducing kernels
Mohammed-Najib BenbourhimLaboratoire MIP-UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, F-31062 Toulouse Cedex 04, FRANCE
bbourhim@cict.fr
(Published online: 13 October 2007)
Abstract
In this paper we propose a constructive method to build vector reproducing kernels.
We define the notion of vector (V,f)-reproducing kernel and we prove that every
vector reproducing kernel is a (V,f)-reproducing kernel. We study the minimal approximation by
these (V,f)-reproducing kernels for different choices of V and f.
Résumé
Dans ce travail on propose une méthode constructive pour générer des noyaux reproduisants vectoriels.
On définit la notion de (V,f)-noyau reproduisant vectoriel et on
montre que tout noyau reproduisant vectoriel est un (V,f)-noyau
reproduisant vectoriel. On étudie l'approximation minimale
à l'aide de ces (V,f)-noyaux reproduisants vectoriels pour
différents choix de V et f.
Mathematics Subject Classification. ???, ???
Key words: vector reproducing kernel, vector (V, f)-reproducing kernel, approximation theory.
© EDP Sciences, ESAIM 2007
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