The Laurent-Horner method for validated evaluation of Chebyshev expansions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929510653362176 |
|---|---|
| author | Aurentz, Jared L. Hashemi, Behnam |
| author_facet | Aurentz, Jared L. Hashemi, Behnam |
| contents | We develop a simple two-step algorithm for enclosing Chebyshev expansions whose cost is linear in terms of the polynomial degree. The algorithm first transforms the expansion from Chebyshev to the Laurent basis and then applies the interval Horner method. It outperforms the existing eigenvalue-based methods if the degree is high or the evaluation point is close to the boundaries of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Laurent-Horner method for validated evaluation of Chebyshev expansions Aurentz, Jared L. Hashemi, Behnam Numerical Analysis We develop a simple two-step algorithm for enclosing Chebyshev expansions whose cost is linear in terms of the polynomial degree. The algorithm first transforms the expansion from Chebyshev to the Laurent basis and then applies the interval Horner method. It outperforms the existing eigenvalue-based methods if the degree is high or the evaluation point is close to the boundaries of the domain. |
| title | The Laurent-Horner method for validated evaluation of Chebyshev expansions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.14952 |