An Adaptive Numerical Integration Algorithm for Simplices

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-ve 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.