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).

翻译：本文提出一种计算Zolotarev有理函数的算法。该算法针对给定阶数的有理函数$r_n^*$，使其在一个集合$E\subseteq\complex\cup\{\infty\}$上的取值相对于另一个集合$F\subseteq\complex\cup\{\infty\}$上的取值尽可能小（即第三类Zolotarev问题）。在计算过程中，我们还对相对于$E$和$F$的符号函数进行了逼近（即第四类Zolotarev问题）。