Volume 38, pp. 146-167, 2011.
Robust rational interpolation and least-squares
Pedro Gonnet, Ricardo Pachón, and Lloyd N. Trefethen
Abstract
An efficient and robust algorithm and a Matlab code ratdisk
are presented for rational interpolation
or linearized least-squares approximation of a function
based on its values at points equally spaced on a circle.
The use of the singular value decomposition enables the detection
and elimination of
spurious poles or Froissart doublets that commonly complicate such
fits without contributing to the quality of the approximation.
As an application, the algorithm leads to a method for the stable
computation of certain radial basis function interpolants in the difficult
case of smoothness parameter
Full Text (PDF) [1.6 MB], BibTeX
Key words
Rational interpolation, spurious poles, Froissart doublets, Padé approximation, radial basis functions, ratdisk, singular value decomposition
AMS subject classifications
41A20, 41A21, 65D05
ETNA articles which cite this article
| Vol. 44 (2015), pp. 593-623 Zlatko Drmač: SVD of Hankel matrices in Vandermonde-Cauchy product form |