Abstract
We prove an analog of Vorpits'kii's theorem for two-dimensional continued fractions, applying the formulas for computing their absolute error.
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Literature Cited
D. I. Bodnar,Branched Continued Fractions [in Russian], Naukova Dumka, Kiev (1986).
D. I. Bodnar, H. Waadeland, Kh. I. Kuchmins'ka, and O. M. Sus', “On the stability of branched continued fractions,”Mat. Met. Fiz.-Mekh. Polya, No. 37, 3–7 (1994).
D. I. Bodnar and Kh. I. Kuchminskaya, “On the convergence of the expansion of a function of two variables into a corresponding branched continued fraction,”Mat. Met. Fiz.-Mekh. Polya, No. 11, 3–6 (1980)
W. Jones and W. Thron,Continued Fractions, Addison-Wesley, Reading, MA (1980).
L. Lorentzen and H. Waadeland,Continued Fractions with Applications, North-Holland, Amsterdam (1992).
Additional information
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 75–83.
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Sus', O.M. Convergence of two-dimensional continued fractions with complex elements. J Math Sci 90, 2385–2392 (1998). https://doi.org/10.1007/BF02433972
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DOI: https://doi.org/10.1007/BF02433972