The generation of lattice points for numerical multiple integration

摘要

A numerical method based on an infinite lattice of quadrature points truncated at some suitable radius has recently been proposed for integrating functions over Rn. Here we show how the lattice points required for this quadrature method may be found by making use of the lattice's generator matrix. The method for generating the lattice points essentially involves solving sets of Diophantine equations by exhaustive search. Timing results indicate that if one was using a lattice method to approximate integrals that arise in practice, then the computation time required to generate the lattice points would not be a major overhead compared to function evaluations.