Transforming low-discrepancy sequences from a cube to a simplex

摘要

Sequences of points with a low discrepancy are the basic building blocks for quasi-Monte Carlo methods. Traditionally these points are generated in a unit cube.To develop point sets on a simplex we will transform the low-discrepancy points from the unit cube to a simplex. An advantage of this approach is that most of the known results on low-discrepancy sequences can be re-used. After introducing several transformations, their efficiency as well as their quality will be evaluated. We present a Koksma–Hlawka inequality which says that under certain conditions the order of convergence using the new point set is the same as that of the original set.