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Why do so many cubature formulae have so many positive weights?

  • Part II Numerical Mathematics
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Abstract

We consider cubature formulae which are invariant with respect to a transformation group and prove sufficient conditions for such formulae to have positive weights. This is worked out for different symmetries: we consider central symmetric, symmetric and fully symmetric cubature formulae. The theoretical results are illustrated with examples.

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Authors and Affiliations

  1. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B3030, Heverlee, Belgium

    Ronald Cools & Ann Haegemans

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  1. Ronald Cools
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  2. Ann Haegemans
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Cools, R., Haegemans, A. Why do so many cubature formulae have so many positive weights?. BIT 28, 791–802 (1988). https://doi.org/10.1007/BF01954899

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  • DOI: https://doi.org/10.1007/BF01954899

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