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TW 371
Tim Pillards and Ronald Cools
Transforming Low-Discrepancy Sequences from a Cube to a Simplex
Abstract
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 for 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 prove 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.
