Advances in Computational Mathematics

, Volume 2, Issue 3, pp 319–341 | Cite as

Acceleration property for the E-algorithm and an application to the summation of series

  • Marc Prévost


The E-algorithm is the most general sequence transformation actually known, since it contains as particular cases almost all the sequence transformations discovered so far: Richardson polynomial extrapolation, Shanks’ transformation, summation processes, Germain-Bonne transformation, Levin’s generalized transformations, the processp and rational extrapolation. In [10] some results concerning the columns of the E-algorithm were proved. In this paper, by adding conditions about determinants, we prove that the diagonal of this algorithm also accelerates the convergence of the initial sequence.


Asymptotic Expansion Initial Sequence Bernoulli Number Acceleration Result Asymptotic Development 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Marc Prévost
    • 1
    • 2
  1. 1.Laboratoire d’Analyse Numérique et d’OptimisationUniversité des Sciences et Technologies de LilleVilleneuve d’Ascq CédexFrance
  2. 2.Bat. H. PoincarréUniversité du Littoral, zone de la mi-voixCalaisFrance

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