An Adaptive Numerical Cubature Algorithm for Simplices

Alan Genz and Ronald Cools

Abstract:
A globally adaptive algorithm for numerical cubature of a vector of
functions over a collection of n-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.

