English

Computation of Zolotarev rational functions

Numerical Analysis 2025-04-03 v2 Numerical Analysis

Abstract

An algorithm is presented to compute Zolotarev rational functions, that is, rational functions rnr_n^* of a given degree that are as small as possible on one set E\complex{}E\subseteq\complex\cup\{\infty\} relative to their size on another set F\complex{}F\subseteq\complex\cup\{\infty\} (the third Zolotarev problem). Along the way we also approximate the sign function relative to EE and FF (the fourth Zolotarev problem).

Keywords

Cite

@article{arxiv.2408.14092,
  title  = {Computation of Zolotarev rational functions},
  author = {Lloyd N. Trefethen and Heather D. Wilber},
  journal= {arXiv preprint arXiv:2408.14092},
  year   = {2025}
}
R2 v1 2026-06-28T18:23:41.714Z