English

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 -Φ\Phi , where Φ\Phi 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.

Keywords

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}
}
R2 v1 2026-06-28T20:40:04.138Z