PIMS/AMI Seminar: Prof. Andriy Prymak

For a domain X with a probability measure pX, consider reconstruction of an unknown function f using discrete least squares approximation from a linear space Vm of dimension m constructed from values f(xi), where xi are randomly drawn from X w.r.t. (X, pX) . Such approximation can be inaccurate when n is close to m. We will present a result quantifying how large should n be for this least squares method to be stable and accurate. It turns out that the deciding quantity is the infimum of the so-called Christoffel function associated with Vm w.r.t. (X, pX). Then we will present our recent results on estimates of behavior of Christoffel function on various convex domains in equipped with the uniform measure.