2019
Том 71
№ 11

All Issues

Sus' О. M.

Articles: 1
Article (Ukrainian)

Approximation Properties of Two-Dimensional Continued Fractions

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

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 30-44

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.