Approximation Theory for Matrices

Details Approximation Theory for Matrices Approximation Theory for Matrices

2004-02-27

arxiv.org/abs/hep-lat/0402037v1

Nucl.Phys.Proc.Suppl. 128C (2004) 107-116

Physics

High Energy Physics

High Energy Physics - Lattice

10 pages, 7 figures

Scientific paper

10.1016/S0920-5632(03)02466-6

We review the theory of optimal polynomial and rational Chebyshev
approximations, and Zolotarev's formula for the sign function over the range
(\epsilon \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.

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