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\leq |z| \leq1). 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.

10 pages, 7 figures

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