Fast and stable rational interpolation in roots of unity and Chebyshev points
In recent years there has been increased interest in rational interpolant which is linear in the interpolated function when the denominator is prescribed see \textit{J.-P. Berrut}, [Comput. Math. Appl. 15, No. 1, 1--16 (1988; Zbl 0646.65006)]. The authors study here a novel solution of the Cauchy interpolation problem. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm presented is particularly simple. Motivation for studying such a problem is derived from the work in NEWLINE[\textit{L. N. Trefethen} et al. \texttt{Chebfun}. Version 4, software collection, (2011), \url{http://www.maths.ox.ac.uk/chebfun/ }]. The algorithms presented here are easy to implement in this system.
scientific article; zbMATH DE number 6070637