Невироджений інтерполяційний ланцюговий дріб

UDC 517.518:519.652 We prove that the Thiele's interpolation continued fraction has either \(2k-1\) approximants when the function is a polynomial of the \(k\)th degree or \(2k\) approximants for the function \(g(z) =a/(z-\alpha)^k.\) We specify the conditions under which the coefficients of the continued fraction are finite and different from zero. For a given set of values of the functions at the nodes, we propose an algorithm that either constructs a nondegenerate interpolation continued fraction or establishes the impossibility of this construction. We also present some examples.