EU Regional School - Maday Seminar- Part2

Location: AICES Graduate School Rogowski Building, Room 115, Schinkelstr. 2, 52062 Aachen

Prof. Yvon Maday - An Empirical Interpolation Procedure: The Magic Points

Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie, Paris

Abstract

Lagrangian interpolation is a classical way to approximate general functions by finite sums of well chosen, pre-definite, linearly independent generating functions; it is much simpler to implement than determining the best fits with respect to some Banach (or even Hilbert) norms. In addition, only partial knowledge is required (here values on some set of points). The problem of defining the best sample of points is nevertheless rather complex and is in general not solved. In this talk we describe a way to derive such sets of points. We do not claim that the points resulting from this construction are optimal in any sense. Nevertheless, the resulting interpolation method is proven to work under certain hypothesis, the process is very general and simple to implement, and compared to situations where the best behavior is known, it is relatively competitive. The application of this interpolation will be presented that allows to treat efficiently non linearities in PDE when discretization with reduced basis methods is performed.