Optimal vertex-modified number-theoretic rules for non-periodic integrands
by
Muni Reddy
University of the South Pacific, Suva, Fiji.
Coauthors: Dr. Stephen Joe (University of Waikato, Hamilton, New Zealand.)

Number-theoretic rules are a class of the so-called lattice rules which are known to be particularly suitable for the approximation of multi-dimensional integrals in which the integrands are periodic. When the integrands are not periodic, then a vertex-modified variant has been proposed. Error bounds for such vertex-modified rules may be obtained in terms of the L₂ discrepancy. In s dimensions these vertex-modified rules contain 2^s weights which may be chosen optimally so that the discrepancy is minimized. We shall compare the average discrepancy for these optimal vertex-modified rules with that for normal number-theoretic and Monte-Carlo rules.

Date received: September 27, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caek-30.