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Computation of an infinite integral using series acceleration

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Abstract

A numerical computation in crystallography involves an infinite integral depending on one parameter. In a recent article in this journal this computational problem is addressed using Romberg’s method and tools for error control. One observe numerical difficulties with the reported approach both near the parameter’s endpoints and near the parameter interval’s midpoint. In this short note we will present an alternative approach making use of a known infinite series formulation of the problem at hand and a simple and efficient series acceleration technique. If some care is taken to avoid cancellations the numerical results are excellent for all values of the parameter.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, Pbox 7800, 5020, Bergen, Norway

    T. O. Espelid

Authors
  1. T. O. Espelid
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Correspondence to T. O. Espelid.

Additional information

Communicated by C. Brezinski

AMS subject classification

65B05, 65B10, 65D30

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Espelid, T.O. Computation of an infinite integral using series acceleration. Numer Algor 40, 17–22 (2005). https://doi.org/10.1007/s11075-005-1514-6

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  • DOI: https://doi.org/10.1007/s11075-005-1514-6

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