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An error estimate for continued fractions


Author: John Gill
Journal: Proc. Amer. Math. Soc. 96 (1986), 71-74
MSC: Primary 40A15; Secondary 30B70
DOI: https://doi.org/10.1090/S0002-9939-1986-0813813-1
MathSciNet review: 813813
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Abstract: New and improved truncation error bounds are derived for continued fractions $ K({a_n}/1)$, where $ {a_n} \to 0$. The geometrical approach is somewhat unusual in that it involves both isometric circles and fixed points of bilinear transformations.


References [Enhancements On Off] (What's this?)

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  • [3] -, Truncation error analysis for continued fractions $ K({a_n}/1)$, where $ \sqrt {\vert{a_n}\vert} + \sqrt {\vert{a_{n-1}}\vert} < 1$, Lecture Notes in Math., vol. 932, Springer-Verlag, Berlin and New York, 1982, pp. 71-73.
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  • [6] W. Thron and W. Waadeland, Accelerating convergence of limit periodic continued fractions $ K({a_n}/1)$, Numer. Math. 34 (1980), 155-170. MR 566679 (81e:30008)
  • [7] -, Truncation error bounds for limit periodic continued fractions, Math. Comp. 40 (1983), 589-597. MR 689475 (84f:30009)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0813813-1
Article copyright: © Copyright 1986 American Mathematical Society

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