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Approximation of functions of several variables by multidimensional $S$-fractions with independent variables

Karpats'kì matematinì publìkacìï, 2021-12, Vol.13 (3), p.592-607 [Peer Reviewed Journal]

ISSN: 2075-9827 ;EISSN: 2313-0210 ;DOI: 10.15330/cmp.13.3.592-607

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  • Title:
    Approximation of functions of several variables by multidimensional $S$-fractions with independent variables
  • Author: Dmytryshyn, R.I. ; Sharyn, S.V.
  • Subjects: algorithm ; branched continued fraction ; continued fraction ; correspondence ; multiple power series
  • Is Part Of: Karpats'kì matematinì publìkacìï, 2021-12, Vol.13 (3), p.592-607
  • Description: The paper deals with the problem of approximation of functions of several variables by branched continued fractions. We study the correspondence between formal multiple power series and the so-called "multidimensional $S$-fraction with independent variables". As a result, the necessary and sufficient conditions for the expansion of the formal multiple power series into the corresponding multidimensional $S$-fraction with independent variables have been established. Several numerical experiments show the efficiency, power and feasibility of using the branched continued fractions in order to numerically approximate certain functions of several variables from their formal multiple power series.
  • Publisher: Vasyl Stefanyk Precarpathian National University
  • Language: English
  • Identifier: ISSN: 2075-9827
    EISSN: 2313-0210
    DOI: 10.15330/cmp.13.3.592-607
  • Source: Open Access: DOAJ Directory of Open Access Journals
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