The Christoffel function: Applications, connections and extensions

Jean-Bernard Lasserre (1, 2)

1 LAAS-POP - Equipe Polynomial OPtimization
2 TSE-R - Toulouse School of Economics

We provide an introduction to the Christoffel function (CF), a well-known (and old) tool from the theory of approximation and orthogonal polynomials. We then describe how it provides a simple and easy-to-use tool to address some problems in data analysis and mining, and in approximation and interpolation of discontinuous functions. Finally we also reveal some surpris- ing links of the CF with seemingly different disciplines, including polynomial optimization, positivity certificates, and equilibrium measures of compact sets

Mots clés: Theory of approximation; Orthogonal polynomials; Reproducing Kernel Hilbert space; Polynomial optimization; Certificates positivity

Domaines: Optimisation et contrôle [math.OC]

Jean-Bernard Lasserre. The Christoffel function: Applications, connections and extensions. Numerical Algebra, Control and Optimization, inPress. ⟨hal-04488686⟩