Approximation by orthonormal polynomials associated with even exponential weights
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912160355975168 |
|---|---|
| author | Grosse, Bastien |
| author_facet | Grosse, Bastien |
| contents | In this paper, we prove a quantitative approximation result by orthonormal polynomials associated to an exponential weight of the form e -$Φ$ , where $Φ$ 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{é} 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation by orthonormal polynomials associated with even exponential weights Grosse, Bastien Numerical Analysis Spectral Theory In this paper, we prove a quantitative approximation result by orthonormal polynomials associated to an exponential weight of the form e -$Φ$ , where $Φ$ 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{é} 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. |
| title | Approximation by orthonormal polynomials associated with even exponential weights |
| topic | Numerical Analysis Spectral Theory |
| url | https://arxiv.org/abs/2412.13603 |