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An acceleration property of theE-algorithm for alternate sequences

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Abstract

We prove a convergence acceleration result by theE-algorithm for sequences whose error has an asymptotic expansion on the scale of comparison for which a determinantal relation holds. This result is generalized to the vector case. Moreover we prove a result which contains an acceleration property for columns and diagonals of theE array. This result is applied to some alternating series.

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique et d'Optimisation, Université des sciences et technologies de Lille, UFR d'IEEA-bat M3, 59655, Villeneuve d'Ascq-Cédex, France

    P. Mortreux

  2. Université du Littoral, Laboratoire de Mathématiques Appliquées, Bât, Poincaré, Centre Universitaire de la Mi-Voix, BP 699, 62228, Calais Cédex, France

    M. Prévost

Authors
  1. P. Mortreux
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  2. M. Prévost
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Communicated by C. Brezinski

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Mortreux, P., Prévost, M. An acceleration property of theE-algorithm for alternate sequences. Adv Comput Math 5, 443–482 (1996). https://doi.org/10.1007/BF02124755

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  • DOI: https://doi.org/10.1007/BF02124755

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