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

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...

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Veröffentlicht in:Karpats'kì matematinì publìkacìï 2021-12, Vol.13 (3), p.592-607
Hauptverfasser: Dmytryshyn, R.I., Sharyn, S.V.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2075-9827
2313-0210
DOI:10.15330/cmp.13.3.592-607