Approximation Properties of Two-Dimensional Continued Fractions - Vozna, S. M.; Kuchmins’ka, Kh. Yo.; Sus' О. M. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
By using the difference formula for approximations of two-dimensional continued fractions, the method of fundamental inequalities, the Stieltjes–Vitali theorem, and generalizations of divided and inverse differences, we estimate the accuracy of approximations of two-dimensional continued fractions with complex elements by their convergents and obtain estimates for the real and imaginary parts of remainders of two-dimensional continued fractions. We also prove an analog of the van Vleck theorem and construct an interpolation formula of the Newton–Thiele type.