Fast Evaluation of Zolotarev Coefficients
arXiv:hep-lat/0402038
Abstract
We review the theory of elliptic functions leading to Zolotarev's formula for the sign function over the range (ε\leq|x| \leq1). We show how Gauss' arithmetico-geometric mean allows us to evaluate elliptic functions cheaply, and thus to compute Zolotarev coefficients ``on the fly'' as a function of (ε). This in turn allows us to calculate the matrix functions (\sgn H), (\sqrt H), and (1/\sqrt H) both quickly and accurately for any Hermitian matrix (H) whose spectrum lies in the specified range.
21 pages, 2 figures. Made various minor corrections