Series Prediction based on Algebraic Approximants

TL;DR

This paper presents a recursive algorithm leveraging Hermite-Padé polynomials for algebraic approximants to predict unknown coefficients in a power series, demonstrated through numerical examples.

Contribution

It introduces a novel recursive method using Hermite-Padé polynomials for algebraic approximants to improve power series coefficient prediction.

Findings

Effective prediction of series coefficients demonstrated

Recursive algorithm shown to be practical

Numerical examples validate the approach

Abstract

It is described how the Hermite-Pad\'e polynomials corresponding to an algebraic approximant for a power series may be used to predict coefficients of the power series that have not been used to compute the Hermite-Pad\'e polynomials. A recursive algorithm is derived and some numerical examples are given.