BIT Numerical Mathematics

, Volume 51, Issue 4, pp 1039–1050

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



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.


Carathéodory-Fejér approximation Near-best rational approximation Chebfun 

Mathematics Subject Classification (2000)

41A50 41A20 


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Copyright information

© Springer Science + Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversiteit AntwerpenAntwerpenBelgium
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK

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