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arXiv · 2408.14092

Computation of Zolotarev rational functions

Lloyd N. Trefethen·Heather D. Wilber
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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).

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Lloyd N. Trefethen, Heather D. Wilber. 2025-04-02. Computation of Zolotarev rational functions. https://arxiv.org/abs/2408.14092

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