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An adaptive numerical integration algorithm for simplices

  • Alan Genz
Track 8: Numerical Analysis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 507)

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.

Keywords

Adaptive Algorithm Subdivision Strategy Cubature Formula Integration Rule Automatic Integration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alan Genz
    • 1
  1. 1.Computer Science DepartmentWashington State UniversityPullman

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