Problem of interpolation of functions by two-dimensional continued fractions

Abstract

The problem of interpolation of functions of two real variables by two-dimensional continued fractions was studied by Kuchmins’ka [1] and Cuyt [2]. Later, this problem was investigated in [3–6], where, in particular, a somewhat different algorithm for the determination of the coefficients of the interpolational two-dimensional continued fraction was proposed and the method was generalized to the problem of interpolation of functions of three real variables by three-dimensional continued fractions. Other types of interpolational two-dimensional continued fractions were considered in [7–9]. In the present paper, we continue the investigations begun in [9].