Approximation of curves with piecewise constant or piecewise linear functions

Frédéric de Gournay (1) , Jonas Kahn (2) , Léo Lebrat (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Analyse numérique [math.NA]

Frédéric de Gournay, Jonas Kahn, Léo Lebrat. Approximation of curves with piecewise constant or piecewise linear functions. 2019. ⟨hal-02284549⟩