Title: A Low Level Introduction to High-Dimensional Sparse Grids

Speaker: John Burkardt, Florida State University

Date/Time: Tuesday, August 21, 2007, 2:00 pm – 3:00 pm

Location: CSRI Building/Room 279 (Sandia NM)

Brief Abstract: This talk is intended to be a very accessible introduction to some of the ideas involved in Smolyak's sparse grid construction for estimating integrals in high dimension.

The integral collects many small items into a single whole. It is the natural way to describe, analyze and simulate geometry, physics, probability, and finance.  Although it was 'discovered' as a tool for physical space, it is essential in higher dimensional abstract spaces, particularly in simulation or the analysis of stochastic processes. 

Approximation techniques must be used for such problems.  In high dimensions, every choice we make comes with very high costs.  We will discuss the accuracy, efficiency, and flexibility of product rules, Monte Carlo, and Quasi Monte Carlo methods.

We will present a sparse grid method that is somewhat like the product rule, with a similar guarantee of accuracy, but at a drastically reduced cost.  We will discuss an application involving a stochastic partial differential equation, in which the higher dimensions represent degrees of freedom in the stochastic disturbance.

CSRI POC: Clayton Webster , (505) 845-3267