Applied Mathematics Seminar on Thursday 12 May 2005

Constructing lattice rules with good bounds on the weighted star discrepancy

• Speaker: A/Professor Stephen Joe, Dept of Mathematics, University of Waikato, Hamilton, New Zealand
• Date: Thursday May 12th
• Time: 11am
• Room: RC-4082

Lattice rules are used to approximate integrals over the d-dimensional unit cube. A measure of the `goodness' of a lattice rule is the
weighted star discrepancy. Averaging arguments show the existence of lattice rules that have good bounds on this quantity. This talk gives an overview of recent results concerning the component by component construction of the
generating vectors for such rules.

We start with the unweighted (classical) star discrepancy and gradually move to the case of general weights. Having such general weights allows us to obtain lattice rules for integrands (such as those arising in some finance
problems) in which it is not the relative importance of the individual variables that matter, but rather the relative importance of distinct groups of variables.