, Volume 51, Issue 4, pp 1039-1050
Date: 04 May 2011

A robust implementation of the Carathéodory-Fejér method for rational approximation

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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.

Communicated by Hans Petter Langtangen.
Research supported by the EPSRC grant EP/E045847/1.