Error estimation in automatic quadrature routines
ACM Transactions on Mathematical Software (TOMS)
Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles
ACM Transactions on Mathematical Software (TOMS)
An adaptive algorithm for the approximate calculation of multiple integrals
ACM Transactions on Mathematical Software (TOMS)
Algorithm 698: DCUHRE: an adaptive multidemensional integration routine for a vector of integrals
ACM Transactions on Mathematical Software (TOMS)
Comments on the Nature of Automatic Quadrature Routines
ACM Transactions on Mathematical Software (TOMS)
Algorithm 824: CUBPACK: a package for automatic cubature; framework description
ACM Transactions on Mathematical Software (TOMS)
An adaptive numerical cubature algorithm for simplices
ACM Transactions on Mathematical Software (TOMS)
Geometrically adaptive numerical integration
Proceedings of the 2008 ACM symposium on Solid and physical modeling
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An adaptive algorithm for computing an approximation to the integral of each element in a vector of functions over a 3-dimensional region covered by simplices is presented. The algorithm is encoded in FORTRAN 77.Locally, a cubature formula of degree 8 with 43 points is used to approximate an integral. The local error estimate is based on the same evaluation points. The error estimation procedure tries to decide whether the approximation for each function has asymptotic behavior, and different actions are taken depending on that decision.The simplex with the largest error is subdivided into 8 simplices. The local procedure is then applied to each new region. This procedure is repeated until convergence.