Problem of interpolation of functions by two-dimensional continued fractions

Interpolation of functionals by integral continued C-fractions

“…investigated in monograph [13]. The coefficients of C-ICF are determined through the interpolation nodes R and the set of values of the function {y i } by means of a finite-continued fraction recurrence…”

“…The purpose of this work is the study of interpolation of a functional given on the continual set of nodes by the integral C-type continued fractions. Such integral continued fractions contains the interpolation continued C-fraction as a particular case, so it is a generalization of one of the types of continued fraction used for interpolation of functions [13].…”

Evaluation of the remainder term for the Thiele interpolation continued fraction

“…and then b k = Φ k [ x 0 , … , x k ], k = 0, 1, … , n, or it is necessary to use the recurrence relations [9,12]:…”

“…Suppose that the function f ( x ) ∈ C ( n + 1 ) ([ α, β ] ) and that the Thiele interpolation continued fraction(10) is constructed according to the values of the function f ( x ) at points of the set Λ. Then the following inequality is true for the remainder term of the Thiele interpolation continued fraction:…”

A New Approach to General Interpolation Formulae for Bivariate Interpolation

“…Symmetric branched continued fraction is a bivariate continued fractions interpolation scheme discussed by Cuyt and Verdonk [2,3], Kučminskaja [4], and Murphy and O'Donohoe [5]. In recent years, Kuchmins'ka and Vozna [6,7], Pahirya [8], Zhao [9], and Wang [10] studied some new kinds of symmetric blending rational interpolation. Wang and Qian studied bivariate polynomial interpolation and continued fractions interpolation over ortho-triples [11].…”