TY - JOUR
AU - Dmytryshyn, R.I.
AU - Sharyn, S.V.
PY - 2021/11/20
Y2 - 2023/09/26
TI - Approximation of functions of several variables by multidimensional $S$-fractions with independent variables
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 13
IS - 3
SE - Scientific articles
DO - 10.15330/cmp.13.3.592-607
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/4995
SP - 592-607
AB - 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.
ER -