Pad\'e-type rational and barycentric interpolation

TL;DR

This paper introduces a Padé-type rational and barycentric interpolation method for functions with specific derivative conditions, demonstrating its effectiveness through numerical examples and applications.

Contribution

It presents a novel interpolation approach that combines Padé-type properties with barycentric methods, including strategies for pole removal and error estimation.

Findings

Numerical examples demonstrate the method's effectiveness.

The interpolation procedure can incorporate partial pole and zero knowledge.

A formula for the error in the real case is established.

Abstract

In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin. Thus, the interpolants constructed in this way possess a Pad\'e--type property at 0. Numerical examples show the interest of the procedure. The interpolation procedure can be easily modified to introduce a partial knowledge on the poles and the zeros of the function to approximated. A strategy for removing the spurious poles is explained. A formula for the error is proved in the real case. Applications are given.