Formula for Hermite multivariate interpolation and partial fraction decomposition

TL;DR

This paper introduces a new explicit formula for Hermite multivariate interpolation and applies it to derive a direct solution for partial fraction decomposition of rational functions, enhancing computational methods in approximation theory.

Contribution

The paper provides a novel explicit formula for Hermite multivariate interpolation within the Chung--Yao framework, linking it to partial fraction decomposition solutions.

Findings

Explicit formula for Hermite multivariate interpolation

Direct solution for partial fraction decomposition of rational functions

Applicable to real case scenarios

Abstract

We present a new formula for the Hermite multivariate interpolation problem in the framework of the Chung--Yao approach. By using the respective univariate interpolation formula, we obtain a direct and explicit solution to the classical partial fraction decomposition problem for rational functions, including the real case.