approximation theory

A remark on Chebyshev rational functions, multipoint Padé approximants and Noise

arXiv:2606.13965

summary

The paper studies Chebyshev rational functions and shows how they generate multipoint Padé approximants, providing recurrence relations and a Thiele-type continued fraction, and examines how noise impacts this interpolation method.

Abstract

Motivated by the recent interest in multipoint Padé approximants in the physics community, we discuss Chebyshev rational functions and show how they give rise to multipoint Padé approximants in exactly the same way that Chebyshev polynomials produce Padé approximants. We present recurrence relations for Chebyshev rational functions, as well as the underlying continued fraction of Thiele type (also known as type). Finally, we provide numerical evidence illustrating the effects of noise on this interpolation scheme and show that a phenomenon similar to that recently observed by Costin, Dunne, and Meynig for Padé approximants also occurs in the multipoint setting.

21 pages, 5 figures

Topics & keywords

#chebyshev rational functions#multipoint pade approximants#continued fractions#noise effects#numerical interpolationChebyshev rational functionsmultipoint Padé approximantsThiele continued fractionR_II typerecurrence relationsnoise analysis
A remark on Chebyshev rational functions, multipoint Padé approximants and Noise · wovepaper