Statistics Seminar: Ian H. Sloan -- The challenge of high-dimensional computation

Ian H.  Sloan School of Mathematics and Statistics University of New South Wales 

Location: Carslaw 173 

Time: 2pm Friday, March 11, 2011 

Title: The challenge of high-dimensional computation 

Abstract: Richard Bellman coined the phrase “the curse of dimensionality” to describe
the extraordinarily rapid increase in the difficulty of typical problems as the number
of variables increases.  A typical problem is numerical multiple integration, where it
is clear that the cost of every integration formula of product type rises exponentially
with the number of dimensions.  Nevertheless, problems with hundreds or even thousands
of variables do arise, and are now being tackled successfully.  In this talk I will
touch briefly on recent advances in understanding and constructing high dimensional
integration rules, but much of the focus will be on applications, in mathematical
finance, linear models in statistics, and flow through random porous media.  A common
theme is that high-dimensional problems present a major challenge for contemporary
computation.