Jean Bernard Lasserre
CNRS and Institute of Mathematics, Toulouse, France
On the Christoffel function and its links with positive polynomials
Streaming link: https://eu.bbcollab.com/guest/895a15724a314ba0ba8c1f5f183b1e19
25 June 2024, 5pm
KU Leuven, Thermotechnisch Instituut
Aula van de Tweede Hoofdwet (01.02)
Abstract
This talk is a brief introduction to the Christoffel-Darboux (CD) kernel and the Christoffel function (CF).
Even though the CD kernel and the CF are well-known tools from approximation theory and orthogonal polynomials, only recently it was realized that they could prove to be very useful (and easy-to-use) in solving some problems in data analysis (e.g outlier detection & support inference). Moreover, we will also show that a non standard use of the CD kernel can provide accurate approximations and interpolations of discontinuous functions. Last but not least we also reveal some (in the author’s opinion) surprising connections of the CF with seemingly unrelated fields (positivity certificates, Pell’s equation, convex duality).
