Computation of Zolotarev Rational Functions
Lloyd N. Trefethen, Heather D. Wilber · SIAM Journal on Scientific Computing · 2025
Abstract. An algorithm is presented to compute Zolotarev rational functions, that is, rational functions [Formula: see text] of a given degree that are as small as possible on one set [Formula: see text] relative to their size on another set [Formula: see text] (the third Zolotarev problem). Along the way we also approximate the sign function relative to [Formula: see text] and [Formula: see text] (the fourth Zolotarev problem).