On the Jacobi formula for Bivariate Pade Approximants of Rectangular Type

TL;DR

This paper introduces a recursive algorithm for multivariate Padé approximants of rectangular type, extending the Jacobi formula, and applies it to solve a Riccati differential equation efficiently.

Contribution

The paper develops a novel recursive algorithm for multivariate Padé approximants of rectangular type, inspired by the Jacobi formula, and demonstrates its application to differential equations.

Findings

Algorithm provides fast and accurate approximations

Effective for solving Riccati differential equations

Extends Jacobi formula to multivariate case

Abstract

In this paper a recursive algorithm is presented for evaluating multivariate Pad\'e approximants (of the rectangular type described in the work of Lutterodt) which is analogous to the Jacobi formula for univariate Pad\'e approximants. This algorithm is then applied to a (singular) Riccati differential equation to generate fast and accurate approximate solutions.