Approximation of Functions of Several Variables by Multidimensional A- and J-fractions with Independent Variables
Numerical Analysis
2023-03-24 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2303.13136,
title = {Approximation of Functions of Several Variables by Multidimensional A- and J-fractions with Independent Variables},
author = {Roman Dmytryshyn and Serhii Sharyn},
journal= {arXiv preprint arXiv:2303.13136},
year = {2023}
}