Lundi 6 décembre salle B014 , 16H00

 Intervenant: Domingo Barrera (Universidad de Granada)
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 Titre:
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 Quelques résultats récents sur la construction de quasi-interpolants splines
 "Some recent results on the construction of spline quasi-interpolants"

 Résumé :
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 The approximation of functions and empirical data is one of the most
 frequent problems arising in practice, and for that purpose multiple
 techniques have been developed. Among them, those based on splines play a
 central role. Frequently data or function are interpolated, making it
 necessary to solve a system of linear (or nonlinear) equations.The
 quasi-interpolating splines provide approximants without solving any
 system, being their coefficients determined directly from the available
 information. Recently new results concerning the construction of discrete
 quasi-interpolant and integrals of small sup norm have been obtained. In
 the case of one variable or for a box spline of two variables explicit
 solutions have been found for the corresponding problems of B-splines of
 low degree. This problem has an independent interest since a small supnorm
 elps to control the error propagation of the approximate data.
 Nevertheless, in order to obtain quasi-interpolants of the mentioned type
 (and also of differential quasi-interpolants) with small constants in the
 error estimates for sufficiently regular functions a specific methodology
 has been considered, in which certain splines independent of the linear
 form involved play an important role. In the usual cases in practice
 (cases $C^{1}$ and $C^{2}$) really small constants are obtained. The most
 recent line of research deals with the construction of non-standard
 quasi-interpolants, starting from a discrete quasi-interpolant with
 certain algebraic precision. The new technique allows to increase the
 precision building for that appropriate  differential quasi-interpolants.