Reducing the construction cost of the component-by-component construction of good lattice rules

@article{Dick2004ReducingTC,
title={Reducing the construction cost of the component-by-component construction of good lattice rules},
author={Josef Dick and Frances Y. Kuo},
journal={Math. Comput.},
year={2004},
volume={73},
pages={1967-1988}
}

The construction of randomly shifted rank-1 lattice rules, where the number of points n is a prime number, has recently been developed by Sloan, Kuo and Joe for integration of functions in weighted Sobolev spaces and was extended by Kuo and Joe and by Dick to composite numbers. To construct d-dimensional rules, the shifts were generated randomly and the generating vectors were constructed component-by-component at a cost of O(n2d2) operations. Here we consider the situation where n is the… CONTINUE READING