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Computational aspects of Boolean cubature

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Abstract

Boolean methods of interpolation [1,4] have been applied to construct multivariate quadrature rules for periodic functions of Korobov classes which are comparable with lattice rules of numerical integration [6,7]. In particular, we introducedd-variate Boolean trapezoidal rules [3,4] andd-variate Boolean midpoint rules [2,4]. The basic tools for constructing Boolean midpoint rules are Boolean midpoint sums. It is the purpose of this paper to use a modification of these Boolean midpoint sums to compute Boolean trapezoidal rules in an efficient way.

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References

  1. G. Baszenski and F.-J. Delvos, Remainders for Boolean interpolation, in:Progress in Approximation Theory, eds. P. Nevai and A. Pinkus (Academic Press, 1991).

  2. G. Baszenski and F.-J. Delvos, Multivariate Boolean midpoint rules, in:Numerical Integration IV, eds. H. Brass and G. Hämmerlin, ISNM 112 (Birkhäuser, Basel, 1993).

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  3. G. Baszenski and F.-J. Delvos, Multivariate Boolean trapezoidal rules, in:Approximation, Probability, and Related Fields, eds. G. Anastassiou and S.T. Rachev (Plenum, New York, 1994).

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  7. I.H. Sloan, Lattice methods for multiple integration: Theory, error analysis and examples, SIAM J. Numer. Anal. 24 (1987).

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Authors and Affiliations

  1. FB Nachrichtentechnik, Fachhochschule Dortmund, Postfach 105018, D-44047, Dortmund, Germany

    Günter Baszenski

  2. FB Mathematik, Universität GH Siegen, Hölderlinstraße 3, D-57076, Siegen, Germany

    Franz-Jürgen Delvos

Authors
  1. Günter Baszenski
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  2. Franz-Jürgen Delvos
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Baszenski, G., Delvos, FJ. Computational aspects of Boolean cubature. Numer Algor 10, 1–11 (1995). https://doi.org/10.1007/BF02198292

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  • DOI: https://doi.org/10.1007/BF02198292

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