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

International audienceThe 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