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BIT Numerical Mathematics

, Volume 7, Issue 2, pp 103–113 | Cite as

On the practical application of the modified romberg algorithm

  • T. Håvie
Article

Abstract

Experience gained in the use of the modified Romberg algorithm is reported. An alternative form of the algorithm based on a cosine transformation of Euler-MacLaurin's and Euler's second formula is discussed. Some examples where the error estimate incorporated in the algorithm partly fails are given. Finally an ALGOL procedure combining the algorithm discussed in a previous paper of the author [1] and the modification discussed in this paper is described.

Key words

Numerical integration extrapolation 

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References

  1. 1.
    Håvie, T.,On a modification of Romberg's algorithm, BIT 6 (1966), 24–30.Google Scholar
  2. 2.
    Smith, F. J.,Quadrature methods based on the Euler-MacLaurin formula and the Clenshaw method of integration, Numerische Mathematik 7 (1965), 406–411.CrossRefGoogle Scholar
  3. 3.
    Jagerman, D.,Introduction of a midpoint formula, Mathematics of Computation, Vol. 20, No. 93 (1966), 79–84.Google Scholar
  4. 4.
    Bauer, F. L., Rutishauser, H., Stiefel, E.,New aspects in numerical quadrature, Proceedings of Symposia in Applied Mathematics, Vol. 15, American Mathematical Society, (1963), 199–218.Google Scholar

Copyright information

© BIT Foundations 1967

Authors and Affiliations

  • T. Håvie
    • 1
  1. 1.Kjeller Computer InstallationKjellerNorway

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