Computation of Zolotarev rational functions
arXiv:2408.14092
Abstract
An algorithm is presented to compute Zolotarev rational functions, that is, rational functions 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 and (the fourth Zolotarev problem).