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Aitken acceleration of some alternating series

  • Part II Numerical Mathematics
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Abstract

Aitken'sδ 2-process is applied to a convergent sequence {s n }, wheres n =u 1 −u 2+...+(−1)n−1 u n . The improvement in the rate of convergence of {s n } is measured in terms of the functionu and its derivatives and numerical examples are given. The paper concludes with a theorem showing that the Aitken process is well-conditioned in such problems and this theorem is shown to have wider applications.

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Authors and Affiliations

  1. The Mathematical Institute, University of St. Andrews, KY16 9SS, St. Andrews, Fife, Scotland

    G. E. Bell & G. M. Phillips

Authors
  1. G. E. Bell
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  2. G. M. Phillips
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Bell, G.E., Phillips, G.M. Aitken acceleration of some alternating series. BIT 24, 70–77 (1984). https://doi.org/10.1007/BF01934516

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  • DOI: https://doi.org/10.1007/BF01934516

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