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Multidimensional regular C-fraction with independent variables corresponding to formal multiple power series

Part of: Holomorphic functions of several complex variables Numerical approximation and computational geometry

Published online by Cambridge University Press:  12 March 2019

R. I. Dmytryshyn
R. I. Dmytryshyn*
Affiliation:
Vasyl Stefanyk Precarpathian National University vul. Shevchenka 57, Ivano-Frankivsk76018, Ukraine (dmytryshynr@hotmail.com)
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Abstract

In the paper the correspondence between a formal multiple power series and a special type of branched continued fractions, the so-called ‘multidimensional regular C-fractions with independent variables’ is analysed providing with an algorithm based upon the classical algorithm and that enables us to compute from the coefficients of the given formal multiple power series, the coefficients of the corresponding multidimensional regular C-fraction with independent variables. A few numerical experiments show, on the one hand, the efficiency of the proposed algorithm and, on the other, the power and feasibility of the method in order to numerically approximate certain multivariable functions from their formal multiple power series.

Keywords

multidimensional regular C-fraction with independent variablesmultiple power seriescorrespondencealgorithm

MSC classification

Primary: 32A17: Special families of functions
Secondary: 32A05: Power series, series of functions 65D15: Algorithms for functional approximation
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 4 , August 2020 , pp. 1853 - 1870
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Copyright
Copyright © Royal Society of Edinburgh 2019

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