Algorithm 816: r2d2lri: an algorithm for automatic two-dimensional cubature

Authors:
Ian Robinson;Michael Hill
Affiliations:
La Trobe University, Victoria, Australia;La Trobe University, Victoria, Australia
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2002

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Abstract

r2d2lri is a non-adaptive algorithm implemented in C++ for performing automatic cubature over a wide variety of finite and non-finite two-dimensional domains. The core integrator uses a sixth-order Sidi transformation applied to a sequence of embedded lattice rules in such a fashion as to incur virtually no computational overhead. Even for integrals over non-finite domains, for which several non-finite to finite transformations may be attempted, the algorithm remains very fast. Performance data are presented which demonstrate both the effectiveness and efficiency of r2d2lri, taking into account the number of function evaluations needed and the execution speed.