Approximation by orthonormal polynomials associated with even exponential weights
Numerical Analysis
2024-12-19 v1 Numerical Analysis
Spectral Theory
Abstract
In this paper, we prove a quantitative approximation result by orthonormal polynomials associated to an exponential weight of the form e - , where is an even polynomial with positive leading coefficient. This result is a consequence of a recursion relation for the orthonormal polynomials and of the strong Poincar{\'e} inequality. Simulations are provided at the end of the article, on smooth, non-smooth functions as well as in the Gaussian and the double well case.
Cite
@article{arxiv.2412.13603,
title = {Approximation by orthonormal polynomials associated with even exponential weights},
author = {Bastien Grosse},
journal= {arXiv preprint arXiv:2412.13603},
year = {2024}
}