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SUMMARY:Quasi-Monte Carlo Methods: From Geometric Discrepancy to High Dime
 nsional Integration - Peter Kritzer (Institute of Financial Mathematics\, 
 University of Linz)
DTSTART:20101126T150000Z
DTEND:20101126T160000Z
UID:TALK27763@talks.cam.ac.uk
CONTACT:Dan Brinkman
DESCRIPTION:Quasi-Monte Carlo (QMC) methods are well known tools which hav
 e been developedfor approximating the value of the integral of a given fun
 ction. Over the past decades\, much progress has been made on numerical in
 tegration by means of QMC methods in various settings. The theory of unifo
 rm distribution modulo one and classical theory on QMC provide many nice p
 roblems and also satisfactory answers for numerical integration algorithms
  in moderate dimension. However\, the question of how to deal with particu
 larly high dimensional problems (i.e.\, the dimension might be in the hund
 reds or thousands) has become a major challenge and is a very active area 
 of research. In our talk\, we are going to discuss some of the key ideas o
 f uniform distribution modulo one and QMC methods\, and point out connecti
 ons to related fields. After a brief overview of some classical concepts a
 nd results\, we are going to present recent developments in the efficient 
 construction and application of high dimensional quasi-Monte Carlo rules. 
 The basic questions we would like to address are:\n\n• What are examples
  of uniformly distributed point sets and QMC rules?\n\n• How can we defi
 ne quality measures for QMC rules?\n     \n• How can we deal with very h
 igh dimensional problems using QMC?\n\nIn particular\, we are going to pre
 sent results on Niederreiter’s digital (t\, m\, s)-nets and (t\, s)-sequ
 ences\, and modifications thereof.\n
LOCATION:MR14\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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