An error estimate for continued fractions

Gill, John

doi:10.1090/S0002-9939-1986-0813813-1

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

[1] L. R. Ford, Automorphic functions, McGraw-Hill, New York, 1929, pp. 23-30.
[2] J. Gill, Converging factors for continued fractions $K({a_n}/1),{a_n} \to 0$ , Proc. Amer. Math. Soc. 84 (1982), 85-88. MR 633283 (82k:30006)
[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.
[4] -, Modifying factors for sequence of linear fractional transformations, Norske Vid. Selsk. Skr. (Trondheim) 3 (1978), 1-7.
[5] W. Jones and R. Snell, Truncation error bounds for continued fractions, SIAM J. Numer. Anal. 6 (1969), 210-221. MR 0247737 (40:1000)
[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)