2017
Том 69
№ 9

All Issues

Approximation Properties of Two-Dimensional Continued Fractions

Kuchmins’ka Kh. Yo., Sus' О. M., Vozna S. M.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 1, pp 36-54.

Citation Example: Kuchmins’ka Kh. Yo., Sus' О. M., Vozna S. M. Approximation Properties of Two-Dimensional Continued Fractions // Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 30-44.

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