Sparse spectral approximations for computing polynomial functionals

Erwan Faou (1, 2) , Fabio Nobile (3) , Christophe Vuillot (1, 4)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 EPFL - Ecole Polytechnique Fédérale de Lausanne
4 ENS Cachan Bretagne - École normale supérieure - Cachan, antenne de Bretagne

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral eigenfunctions that turns out to be satisfied in many cases, including the Fourier and Hermite basis.

Mots clés: Spectral methods; Sparse representations; Hermite polynomials

Domaines: Analyse numérique [math.NA]

Erwan Faou, Fabio Nobile, Christophe Vuillot. Sparse spectral approximations for computing polynomial functionals. 2012. ⟨hal-00718307⟩