Geodesic
Quasi-interpolants splines : exemples et applications
Paul Sablonnière1
1 Paul Sablonnière, Centre de mathématiques, INSA de Rennes, 20 avenue des Buttes de Coësmes, CS 14315, 35043 Rennes cédex, France. e-mail : psablonn@insa-rennes.fr
ESAIM. Proceedings, Tome 20 (2007), pp. 195-207.

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A quasi-interpolant (abbr. QI) is an approximation operator obtained as a finite linear combination of basis functions with bounded support (B-splines). In addition, the coefficient of a B-spline is a linear functional (of differential, discrete or integral type) acting on the function to be approximated in a neighbourhood of the support of that B-spline. The big advantage of this approach is that the computation of a QI is direct and does not need the solution of any system of equations, unlike what happens with interpolants. It is particularly interesting in the bivariate or trivariate cases, where the number of B-splines can be rather large. In this paper, I present some examples of QIs of different types on spaces of univariate or multivariate splines. Then, I give some applications to approximation and numerical analysis.
DOI : 10.1051/proc:072017

Paul Sablonnière 1

1 Paul Sablonnière, Centre de mathématiques, INSA de Rennes, 20 avenue des Buttes de Coësmes, CS 14315, 35043 Rennes cédex, France. e-mail : psablonn@insa-rennes.fr 
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Paul Sablonnière. Quasi-interpolants splines : exemples et applications. ESAIM. Proceedings, Tome 20 (2007), pp. 195-207. doi : 10.1051/proc:072017. http://geodesic.mathdoc.fr/articles/10.1051/proc:072017/

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