Sparse spectral approximations for computing polynomial functionals

2012/07/16 by Erwan Faou, Fabio Nobile, Faou, Erwan +3
Computer Science · Mathematics · Physics and Astronomy · #33C45 #65D15 #65M70 #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1207.3728

openalex publication_date 2012/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• Birkhoff Normal Form and Hamiltonian PDEs

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