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1st Joint International Meeting between the American Mathematical Society and the New Zealand Mathematical Society
December 12-15, 2007
Victoria University of Wellington
Wellington, New Zealand

Organizers
Peter Donelan (VUW, co-convener), Matt Miller (South Carolina, co-convener), Jeff Cheeger (Courant/NYU), Rod Downey (VUW), Peter Jones (Yale), Vaughan Jones (UC Berkeley), Gaven Martin (Massey, Albany)

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Lattice rules for integration over Rs
by
Stephen Joe
University of Waikato
Coauthors: Vasile Sinescu

There has been much work done on lattice rules for the numerical approximation of integrals defined over the s-dimensional unit cube. If the integration region happens to be Rs, it is quite common to apply some transformation to map Rs to the unit cube in order to make use of these lattice rules.

However, there do exist lattice rules for Rs. A natural question that arises is whether these lattice rules have merit for approximating integrals over Rs.

We review some known results for these lattice rules and present some new preliminary theoretical results based on Fourier transforms and reproducing kernel Hilbert spaces.

Date received: September 25, 2007

Copyright © 2007 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 # catm-68.