Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.02639 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910320252944384 |
|---|---|
| author | Krieg, David Vybiral, Jan |
| author_facet | Krieg, David Vybiral, Jan |
| contents | We study the integration problem on Hilbert spaces of (multivariate) periodic functions. The standard technique to prove lower bounds for the error of quadrature rules uses bump functions and the pigeon hole principle. Recently, several new lower bounds have been obtained using a different technique which exploits the Hilbert space structure and a variant of the Schur product theorem. The purpose of this paper is to (a) survey the new proof technique, (b) show that it is indeed superior to the bump-function technique, and (c) sharpen and extend the results from the previous papers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02639 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New lower bounds for the integration of periodic functions Krieg, David Vybiral, Jan Numerical Analysis We study the integration problem on Hilbert spaces of (multivariate) periodic functions. The standard technique to prove lower bounds for the error of quadrature rules uses bump functions and the pigeon hole principle. Recently, several new lower bounds have been obtained using a different technique which exploits the Hilbert space structure and a variant of the Schur product theorem. The purpose of this paper is to (a) survey the new proof technique, (b) show that it is indeed superior to the bump-function technique, and (c) sharpen and extend the results from the previous papers. |
| title | New lower bounds for the integration of periodic functions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2302.02639 |