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An adaptive numerical integration algorithm for simplices

  • Track 8: Numerical Analysis
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Computing in the 90's (Great Lakes CS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 507))

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Abstract

A globally adaptive algorithm for numerical multiple integration over an n-dimensional simplex is described. The algorithm is based on a subdivision strategy that chooses for subdivision at each stage the subregion (of the input simplex) with the largest estimated error. This subregion is divided in half by bisecting an edge. The edge is chosen using information about the smoothness of the integrand. The algorithm uses a degree seven-five integration rule pair for approximate integration and error calculation, and a heap for a subregion data structure. Test results are presented and discussed where the algorithm is used to compute approximations to integrals used for estimation of eigenvalues of a random covariance matrix.

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Author information

Authors and Affiliations

  1. Computer Science Department, Washington State University, 99164-1210, Pullman, WA

    Alan Genz

Authors
  1. Alan Genz
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Editor information

Naveed A. Sherwani Elise de Doncker John A. Kapenga

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© 1991 Springer-Verlag Berlin Heidelberg

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Genz, A. (1991). An adaptive numerical integration algorithm for simplices. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038504

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  • DOI: https://doi.org/10.1007/BFb0038504

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97628-0

  • Online ISBN: 978-0-387-34815-5

  • eBook Packages: Springer Book Archive

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