Approximation Properties of Two-Dimensional Continued Fractions

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


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.
How to Cite
Vozna, S. M., K. Y. Kuchmins’ka, and Sus’О. M. “Approximation Properties of Two-Dimensional Continued Fractions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 1, Jan. 2003, pp. 30-44,
Research articles