Approximation of curves with piecewise constant or piecewise linear functions
Numerical Analysis
2019-09-11 v1 Numerical Analysis
Abstract
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 -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.
Cite
@article{arxiv.1909.04582,
title = {Approximation of curves with piecewise constant or piecewise linear functions},
author = {Frédéric de Gournay and Jonas Kahn and Léo Lebrat},
journal= {arXiv preprint arXiv:1909.04582},
year = {2019}
}