Open AccessApproximation of functions of several variables by multidimensional $S$-fractions with independent variables
Author(s) -
R. I. Dmytryshyn,
S. V. Sharyn
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.3.592-607
Subject(s) - mathematics , formal power series , fraction (chemistry) , series (stratigraphy) , variables , power series , power (physics) , statistics , mathematical analysis , paleontology , chemistry , physics , organic chemistry , quantum mechanics , biology
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.