Abstract:
A globally adaptive algorithm for numerical cubature of a vector
of functions over a collection of
dimensional simplices is described.
The algorithm is based on a subdivision strategy that chooses for subdivision
at each stage the subregion (of the input simplices) with the largest
estimated error. This subregion is divided into two, three or four equal volume
subregions by cutting selected edges. These edges are selected using
information about the smoothness of the integrands in the edge directions. The
algorithm allows a choice from several embedded cubature rule sequences for
approximate integration and error estimation. A Fortran 95 implementation as
a part of CUBPACK is also discussed. Testing of the algorithm is described.
G.1.4Numerical AnalysisQuadrature and Numerical Differentiation
[adaptive quadrature; multiple quadrature]
G.4Mathematical Software
[efficiency; reliability and robustness]
Cubature, Simplex, Software
adaptive integration, cubature, multidimensional integration, simplex
An Adaptive Numerical Cubature Algorithm
for Simplices
Alan Genz
Department of Mathematics, Washington State University, USA

Ronald Cools
Department of Computer Science, Katholieke Universiteit Leuven, Belgium
20030217