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A robust implementation of the Carathéodory-Fejér method

By Joris van Deun and Lloyd N. Trefethen

Abstract

Best rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Carathéodory-Fejér (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software

Topics: Numerical analysis
Publisher: Springer
Year: 2010
OAI identifier: oai:generic.eprints.org:926/core69

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