Mathematics of Computation

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Index-doubling in sequences by Aitken extrapolation

Author(s): Roger Alexander.
Journal: Math. Comp. 72 (2003), 1947-1961.
MSC (2000): Primary 65B05, 11A55
Posted: May 14, 2003
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Abstract | References | Similar articles | Additional information

Abstract: Aitken extrapolation, applied to certain sequences, yields the even-numbered subsequence of the original. We prove that this is true for sequences generated by iterating a linear fractional transformation, and for some sequences of convergents of the regular continued fractions of certain quadratic irrational numbers.

References:

[Br 1991]: Claude Brezinski and Michela Redivo Zaglio, Extrapolation Methods: Theory and Practice. New York: Elsevier, 1991. MR 93d:65001
[BL 1986]: C. Brezinski and A. Lembarki, ``Acceleration of extended Fibonacci sequences.'' Appl. Numer. Math. 2 (1986) pp. 1-8. MR 87k:65005
[MP 1985]: J. H. McCabe and G. M. Phillips, ``Aitken Sequences and Generalized Fibonacci Numbers.'' Math. Comput. 45 (1985) pp. 553-558. MR 87b:41015
[Pe 1929]: Oskar Perron, Die Lehre von den Kettenbrüchen. Leipzig: B. G. Teubner, 1929. MR 12:254b; MR 16:239e; MR 19:25c (later editions).
[Ph 1984]: G. M. Phillips, ``Aitken Sequences and Fibonacci Numbers.'' Amer. Math. Monthly 91 No. 6 (1984), 354-357. MR 85h:65013


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