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：本文提出了一种计算佐洛塔廖夫有理函数的算法，即计算给定次数的有理函数 $r_n^*$，使其在一个集合 $E\subseteq\complex\cup\{\infty\}$ 上的值相对于其在另一个集合 $F\subseteq\complex\cup\{\infty\}$ 上的值尽可能小（佐洛塔廖夫第三问题）。在此过程中，我们还近似了相对于 $E$ 和 $F$ 的符号函数（佐洛塔廖夫第四问题）。