Approximation of Functions of Several Variables by Multidimensional A- and J-fractions with Independent Variables

TL;DR

This paper introduces a generalized algorithm for approximating multivariable functions using multidimensional A- and J-fractions with independent variables, supported by numerical experiments demonstrating effectiveness.

Contribution

It extends Gragg's algorithm to compute coefficients of multidimensional continued fractions from formal series, enabling new approximation methods for multivariable functions.

Findings

Algorithm successfully computes coefficients for multidimensional A- and J-fractions.

Numerical experiments validate the approximation approach.

Method offers a new tool for multivariable function approximation.

Abstract

The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is constructed that enables us to compute, by the coefficients of the given formal multiple power series, the coefficients of the corresponding multidimensional A-fraction with independent variables. This algorithm can also be used to construct the multidimensional J-fraction with independent variables corresponding to a given formal multiple Laurent series. Some numerical experiments of approximating the functions of several variables by these branched continued fractions are given.