Introduction to kernel-based methods

Wednesday 18 March 2015 h. 14:30, room 2BC30
Gabriele Santin (Padova, Dip. Mat.)
"Introduction to kernel-based methods"

Abstract
In this talk we give an introduction to kernel-based methods and to their application in different fields of applied mathematics.
We consider some examples that motivate the use of kernel-based techniques. Each example can be included in the same framework, but allows to show and discuss different features that arise naturally in the particular application. The examples deal with multivariate scattered data approximation, optimal recovery in Hilbert spaces, numerical solution of PDE, machine learning, and statistics.
After building up the fundamental tools of kernel-based methods, we will introduce the problem of the determination of optimal subspaces for kernel-based multivariate approximation. We will give some insight into the problem and discuss possible applications.