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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
MathSciNet review:
1986814
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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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Additional Information:
Roger
Alexander
Affiliation:
Department of Mathematics, 400 Carver Hall, Iowa State University, Ames, Iowa 50011
Email:
alex@iastate.edu
DOI:
10.1090/S0025-5718-03-01560-6
PII:
S 0025-5718(03)01560-6
Keywords:
Aitken extrapolation,
linear fractional transformation,
periodic continued fraction
Received by editor(s):
January 4, 2002
Posted:
May 14, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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