# Lifting the Curse of Dimensionality: Numerical Integration in High Dimensions

#### by Professor Ian Sloan

Institution: School of Mathematics, University of NSW
Date: Wed 28th March 2007
Time: 11:00 AM
Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne

Abstract: Richard Bellmann coined the phrase the curse of
dimensionality" to describe the extraordinarily rapid increase in the difficulty of most problems as the number of variables increases. A typical problem is numerical multiple integration, where the cost of any integration formula of product type obviously rises exponentially with the number of variables. Nevertheless, problems with hundreds or even thousands of variables do arise, and
are now being tackled successfully. In this talk I will tell the story of recent developments, in which in less than a decade the focus has
turned from existence theorems to concrete constructions that
achieve the theoretically predicted results even for integrals in thousands of dimensions with many thousands of points. Suitable integration rules of this kind are now being applied to applications from mathematical finance.