Fast Evaluation of Zolotarev Coefficients
Abstract
We review the theory of elliptic functions leading to Zolotarev's formula for the sign function over the range (ε ≤|x| ≤1). 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 ( H), ( H), and (1/ H) both quickly and accurately for any Hermitian matrix (H) whose spectrum lies in the specified range.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.