TITLE:  Some Recent Insights into Computing with Positive Definite Kernels

ABSTRACT:

In this talk I will discuss recent joint work with Mike McCourt (SigOpt, San Francisco) that has led to progress on the numerically stable computation of certain quantities of interest when working with positive definite kernels to solve scattered data interpolation (or kriging) problems.

In particular, I will draw upon insights from both numerical analysis and modeling with Gaussian processes which will allow us to connect quantities such as, e.g., (deterministic) error estimates in terms of the power function with the kriging variance. This provides new kernel parametrization criteria as well as new ways to compute known criteria such as MLE. Some numerical examples will illustrate the effectiveness of this approach.

Bio:  Greg Fasshauer is a professor in the Department of Applied Mathematics at the Illinois Institute of Technology in Chicago. He earned his PhD in Mathematics from Vanderbilt University in 1995 and joined IIT in 1997 after spending two years as a visiting assistant professor at Northwestern University.  His research focuses on numerical analysis, computation and approximation theory with a special emphasis on kernel-based approximation. Among other things, he has published two monographs on this subject, most recently a joint publication with Mike McCourt entitled “Kernel-based Approximation Methods using MATLAB”.