A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

Antonio Falco (1) , Anthony Nouy (2)

1 CEU-UCH - Universidad Cardenal Herrera-CEU
2 GeM - Institut de Recherche en Génie Civil et Mécanique

The Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial dierential equations (PDE) dened in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, we introduce a generalization of Eckart and Young theorem which allows to prove the convergence of the so-called progressive PGD for a large class of linear problems dened in tensor product Hilbert spaces.

Mots clés: Proper Generalized Decomposition; Singular Values; Tensor Product Hilbert Spaces; Separated representation

Domaines: Analyse numérique [math.NA]

Antonio Falco, Anthony Nouy. A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach. Journal of Mathematical Analysis and Applications, 2011, 376 (2), pp.469-480. ⟨hal-00461094v2⟩