Extracting classical solutions from « truncated moment solutions » of weak formulations of some ODEs and PDEs.

Jean Lasserre
Université de Toulouse III (Paul Sabatier)

Let « mu » be a Borel measure on a compact space Y \times X\times [0,1]
whose marginal on X \times [0,1] is the Lebesgue measure. In addition
assume that « mu » is supported on the graph { (y(x,t),x,t): (x,t) in X \times [0,1] }
of a function (x,t) -> y(x,t), and we have only access to all moments of « mu »
up to order 2d. We provide a new methodology to extract the function y from this moment-based
information. It is based on the Christoffel function associated with « mu » and relatively simple
to implement. One of its attractive features confirmed in preliminary experimental results
is to strongly attenuate the Gibbs phenomenon usually inherent to methods that approximate y(x,t)
with polynomials (e.g., typically the case when y is a discontinuous solution of some PDE).

Joint work with D. Henrion, S. Marx, E. Pauwels and T. Weisser.

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