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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Index-doubling in sequences by Aitken extrapolation


Author: Roger Alexander
Journal: Math. Comp. 72 (2003), 1947-1961
MSC (2000): Primary 65B05, 11A55
Published electronically: 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.


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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: http://dx.doi.org/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
Published electronically: May 14, 2003
Article copyright: © Copyright 2003 American Mathematical Society