Computation of Zolotarev rational functions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913771002265600 |
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| author | Trefethen, Lloyd N. Wilber, Heather D. |
| author_facet | Trefethen, Lloyd N. Wilber, Heather D. |
| contents | An algorithm is presented to compute Zolotarev rational functions, that is, rational functions $r_n^*$ of a given degree that are as small as possible on one set $E\subseteq\complex\cup\{\infty\}$ relative to their size on another set $F\subseteq\complex\cup\{\infty\}$ (the third Zolotarev problem). Along the way we also approximate the sign function relative to $E$ and $F$ (the fourth Zolotarev problem). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computation of Zolotarev rational functions Trefethen, Lloyd N. Wilber, Heather D. Numerical Analysis 30E10, 41A20, 65D15 An algorithm is presented to compute Zolotarev rational functions, that is, rational functions $r_n^*$ of a given degree that are as small as possible on one set $E\subseteq\complex\cup\{\infty\}$ relative to their size on another set $F\subseteq\complex\cup\{\infty\}$ (the third Zolotarev problem). Along the way we also approximate the sign function relative to $E$ and $F$ (the fourth Zolotarev problem). |
| title | Computation of Zolotarev rational functions |
| topic | Numerical Analysis 30E10, 41A20, 65D15 |
| url | https://arxiv.org/abs/2408.14092 |