Algorithm 906: elrint3d - A Three-Dimensional Nonadaptive Automatic Cubature Routine Using a Sequence of Embedded Lattice Rules

摘要

A three-dimensional automatic cubature routine, called elrint3d, is described and numerical results are presented that demonstrate its applicability across a wide range of domains and integrand types. The underlying algorithm is based on a 2~s-copy lattice augmentation sequence, the seed lattice for which has been determined by exhaustive search based on optimization of index of merit and trigonometric degree of precision.