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

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2020-08, Vol.150 (4), p.1853-1870 [Peer Reviewed Journal]

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Title:
Multidimensional regular C-fraction with independent variables corresponding to formal multiple power series
Author: Dmytryshyn, R. I.
Subjects: Algorithms ; Independent variables ; Power series
Is Part Of: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2020-08, Vol.150 (4), p.1853-1870
Description: 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.
Publisher: Edinburgh, UK: Royal Society of Edinburgh Scotland Foundation
Language: English
Identifier: ISSN: 0308-2105
EISSN: 1473-7124
DOI: 10.1017/prm.2019.2
Source: ProQuest Central

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