PGD Versus SVD

Abstract

The issue of separability is of major importance when using the Proper Generalized Decomposition. Efficient computer implementations require the separated representation of model parameters, boundary conditions and/or source terms. This can be performed by applying the Singular Value Decomposition (SVD) or its multi-dimensional counterpart, the so-called High Order Singular Value Decomposition. This chapter revisits these concepts. We then point out and discuss the subtle connections between SVD and PGD. This allows us to illustrate how the PGD solver can compress separated representations, and also to justify the fact that in certain circumstances the PGD solution procedure can be viewed as the calculation of an on-the-fly compressed representation.