Padua points: theory, computation and applications

The Faculty of Informatics is pleased to announce a seminar given by Stefano De Marchi

DATE: Friday, May 15th 2010
PLACE: USI Università della Svizzera italiana, room SI-008, Informatics building (Via G. Buffi 13)
TIME: 15.30

ABSTRACT:
The problem of choosing good nodes on a given compact set is a central one in multivariate polynomial interpolation. Besides unisolvence, which is by no means an easy problem, for practical purposes one needs slow growth of the Lebesgue constant and computational efficiency. In this talk, we present the family of Padua points, a set of unisolvent points in the square [-1, 1]^2, which show Lebesgue constants with minimal order of growth O(log^2(n)) (n the degree of the interpolating polynomial).
We also discuss recent developments in the efficient computation of polynomial interpolation and cubature based on these points.

BIO:
Stefano De Marchi is an associate professor in Numerical Analysis at the University of Padua, Italy. His research interests focus on multivariate polynomial and Radial Basis Functions (RBF) approximation. Nearly-optimal points for polynomial (Padua points) and RBF approximation is the topic where he has mostly concentrated his research in the last 7 years, thanks to the fruithfull collaboration with the Constructive Approximation and its Applications group between the Universities of Padua and Verona. He also contributed to the development of efficient software for the computation of polynomial (hyper)interpolants and related cubature formulae on 2-d and 3-d domains on nearly-optimal points. Dr. De Marchi received his Ph.D. from the University of Padua in 1994. He became assistant professor at the University of Udine (Italy) in 1995. Then, in 2001, he moved to the University of Verona where he became associate professor in 2005. He is founder and editor in chief of the e-journal, Dolomites Research Notes on Approximation.

HOST: Prof. Kai Hormann