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                <term xml:lang="en">Singular Values</term>
                <term xml:lang="en">Tensor Product Hilbert Spaces</term>
                <term xml:lang="en">Separated representation</term>
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              <p>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.</p>
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