Prony's method in several variables: symbolic solutions by universal interpolation

TL;DR

This paper explores a symbolic approach to multivariate Prony's method, linking it to polynomial interpolation and universal interpolation concepts, providing estimates on the minimal evaluations required for solutions.

Contribution

It introduces a symbolic framework for multivariate Prony's method using universal interpolation, extending univariate Chebyshev system ideas and estimating minimal evaluation counts.

Findings

Establishes a connection between Prony's method and multivariate polynomial interpolation.

Provides estimates on the minimal number of evaluations needed.

Introduces a symbolic approach based on universal interpolation.

Abstract

The paper considers a symbolic approach to Prony's method in several variables and its close connection to multivariate polynomial interpolation. Based on the concept of universal interpolation that can be seen as a weak generalization of univariate Chebychev systems, we can give estimates on the minimal number of evaluations needed to solve Prony's problem.