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On the Construction of Cubature Formulae with Few Nodes Using Groebner Bases

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Numerical Integration

Part of the book series: NATO ASI Series ((ASIC,volume 203))

Abstract

One method for constructing cubature formulae of a given degree of precision consists of using the common zeros of a finite set F of polynomials as nodes. The formula exists if and only if F is an H-basis and some well-defined orthogonality conditions hold. Groebner bases and especially Buchberger’s algorithm for their computation allow an effective calculation of H-bases and easy proofs and generalizations of known methods based on H-bases. Groebner bases, a powerful tool in Computer Algebra for analyzing ideals and solving systems of algebraic equations, allow in addition the calculation of the common zeros of the polynomials in F also in cases, where the number of unknowns is different from the number of equations.

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Author information

Authors and Affiliations

  1. FB Mathematik und Informatik, FernUniversität Hagen, Postfach 940, 5800, Hagen 1, F.R. Germany

    H. Michael Möller

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  1. H. Michael Möller
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada

    Patrick Keast

  2. Departments of Mathematics and Engineering Mechanics, University of Kentucky, Lexington, Kentucky, USA

    Graeme Fairweather

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© 1987 D. Reidel Publishing Company

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Möller, H.M. (1987). On the Construction of Cubature Formulae with Few Nodes Using Groebner Bases. In: Keast, P., Fairweather, G. (eds) Numerical Integration. NATO ASI Series, vol 203. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3889-2_19

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  • DOI: https://doi.org/10.1007/978-94-009-3889-2_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8227-3

  • Online ISBN: 978-94-009-3889-2

  • eBook Packages: Springer Book Archive

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