Computation of Zolotarev rational functions
Abstract
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).
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.14092
- arXiv:
- arXiv:2408.14092
- Bibcode:
- 2024arXiv240814092T
- Keywords:
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- Mathematics - Numerical Analysis;
- 30E10;
- 41A20;
- 65D15