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Introductory Remarks The Cubature Research Group is based at the
Department of Computer Science and Computer Engineering La Trobe University Bundoora, 3086 Victoria Australia The group’s research centres on the development of quality software for the evaluation of quadratures and cubatures in moderately low dimensions. Currently, the group’s focus is upon the use of lattice-based rules in general-purpose cubature algorithms. Until recently, lattice cubature rules have not been considered suitable candidates upon which one can build efficient, effective and reliable low-dimensional cubature algorithms, their theoretical strengths (supposedly) coming to the fore only in high-dimensional problems. However, through efficient use of lattice rules with high indices of merit, combined with optimal use of transformations and carefully crafted heuristic error estimates, two very successful general-purpose routines have been developed: r2d2lri in two dimensions and elrint3d in three dimensions. The code for these algorithms and other information relevant to the group's activities are available via the links on the left of this page.
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