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.
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Kuchmins'ka, K.I., Sus', O.M. & Vozna, S.M. Approximation Properties of Two-Dimensional Continued Fractions. Ukrainian Mathematical Journal 55, 36–54 (2003). https://doi.org/10.1023/A:1025016501397
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DOI: https://doi.org/10.1023/A:1025016501397