Quadrature formulas from rational approximations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918098834030592 |
|---|---|
| author | Horning, Andrew Trefethen, Lloyd N. |
| author_facet | Horning, Andrew Trefethen, Lloyd N. |
| contents | It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new method to derive all kinds of quadrature formulas as well as fundamental insight into the mathematics of quadrature. Intervals or curves of quadrature nodes correspond to near-optimal branch cuts of the Cauchy transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadrature formulas from rational approximations Horning, Andrew Trefethen, Lloyd N. Numerical Analysis 41A20 It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new method to derive all kinds of quadrature formulas as well as fundamental insight into the mathematics of quadrature. Intervals or curves of quadrature nodes correspond to near-optimal branch cuts of the Cauchy transform. |
| title | Quadrature formulas from rational approximations |
| topic | Numerical Analysis 41A20 |
| url | https://arxiv.org/abs/2507.14971 |