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Index-doubling in sequences by Aitken extrapolation


Author: Roger Alexander
Journal: Math. Comp. 72 (2003), 1947-1961
MSC (2000): Primary 65B05, 11A55
DOI: https://doi.org/10.1090/S0025-5718-03-01560-6
Published electronically: May 14, 2003
MathSciNet review: 1986814
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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 [Enhancements On Off] (What's this?)

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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: https://doi.org/10.1090/S0025-5718-03-01560-6
Keywords: Aitken extrapolation, linear fractional transformation, periodic continued fraction
Received by editor(s): January 4, 2002
Published electronically: May 14, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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