sparse_2012_scala


sparse_2012_scala, "Sparse Grid Collocation for Uncertainty Quantification", a talk at the SCALA Conference 2012 (Scientific Computing Around Louisiana), held at Louisiana State University in Baton Rouge, on 20/21 January 2012.

This talk will start by mentioning examples of a few stochastic problems. We'll show how integration is used as a means of averaging out the uncertainties, and consider the behavior of product rules and Monte Carlo methods for estimating integrals. We'll suggest that the accuracy of the product rule can be achieved at a much lower cost, by using Smolyak's sparse grid definition. We'll then look at a common form of the sparse grid based on the Clenshaw Curtis rule. We'll finish with some numerical examples that emphasize how nice it is to have something converge quickly in a high dimensional space.

The following files were used:


Last revised on 05 February 2024.