 CARMA COLLOQUIUM
 Speaker: Josef Dick, School of Mathematics and Statistics, University of NSW
 Title: Highdimensional Numerical Integration
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 16^{th} Jun 2011
 Abstract:
Highdimensional integrals come up in a number of applications like statistics, physics and financial mathematics. If explicit solutions are not known, one has to resort to approximative methods. In this talk we will discuss equalweight quadrature rules called quasiMonte Carlo. These rules are defined over the unit cube $[0,1]^s$ with carefully chosen quadrature points. The quadrature points can be obtained using numbertheoretic and algebraic methods and are designed to have low discrepancy, where discrepancy is a measure of how uniformly the quadrature points are distributed in $[0,1]^s$. In the onedimensional case, the discrepancy coincides with the KolmogorovSmirnov distance between the uniform distribution and the empirical distribution of the quadrature points and has also been investigated in a paper by Weyl published in 1916.
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