Pade and Hermite-Pade approximation and orthogonality

TL;DR

This paper introduces Pade and Hermite-Pade approximation methods, emphasizing the role of orthogonality and potential theory in understanding their asymptotic behavior and convergence properties.

Contribution

It provides a concise overview of Pade and Hermite-Pade approximations, highlighting the importance of orthogonality and potential theory in their analysis.

Findings

Orthogonality is crucial in Pade and Hermite-Pade approximation analysis.

Logarithmic potential theory helps describe asymptotic behavior.

Insights into convergence properties of rational approximations.

Abstract

We give a short introduction to Pade approximation (rational approximation to a function with close contact at one point) and to Hermite-Pade approximation (simultaneous rational approximation to several functions with close contact at one point) and show how orthogonality plays a crucial role. We give some insight into how logarithmic potential theory helps in describing the asymptotic behavior and the convergence properties of Pade and Hermite-Pade approximation.