Approximation Theory for Matrices
Abstract
We review the theory of optimal polynomial and rational Chebyshev approximations, and Zolotarev's formula for the sign function over the range (ε ≤ |z| ≤1). We explain how rational approximations can be applied to large sparse matrices efficiently by making use of partial fraction expansions and multi-shift Krylov space solvers.
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.