Approximation of curves with piecewise constant or piecewise linear functions

de Gournay, Frédéric; Kahn, Jonas; Lebrat, Léo

Document type :

Pré-publication ou Document de travail

Title :

Approximation of curves with piecewise constant or piecewise linear functions

Author(s) :

de Gournay, Frédéric [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Kahn, Jonas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Lebrat, Léo [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In this paper we compute the Hausdorff distance between sets of continuous curves and sets of piecewise constant or linear discretizations. These sets are Sobolev balls given by the continuous or discrete L p-norm of the ...
Show more >In this paper we compute the Hausdorff distance between sets of continuous curves and sets of piecewise constant or linear discretizations. These sets are Sobolev balls given by the continuous or discrete L p-norm of the derivatives. We detail the suitable discretization or smoothing procedure which are preservative in the sense of these norms. Finally we exhibit the link between Eulerian numbers and the uniformly space knots B-spline used for smoothing.Show less >

Language :

Anglais

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