A priori tensor approximations for the numerical solution of high dimensional problems: alternative definitions
Résumé
Model reduction techniques based on the construction of separated representations are receiving a growing interest in scientific computing. A family of methods, recently called Proper Generalized Decomposition (PGD) methods, have been introduced for the a priori construction of separated representations of the solution of problems defined in tensor product spaces. Different definitions of PGDs and associated algorithms have been proposed. Here, we review classical definitions of progressive PGDs and we introduce several variants in order to improve convergence properties. In particular, we introduce the Minimax PGD, recently proposed for evolution problems, which can be interpreted as a Petrov-Galerkin model reduction technique. The different variants are presented in an abstract setting. Model examples will illustrate some properties of the different variants of PGDs.
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