Approximation Theory for Matrices
A. D. Kennedy
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.
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