Abstract
Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called proper generalized decompositions (PGD) methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analysis of a family of progressive and updated PGDs for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banach space.
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This work is supported by the ANR (French National Research Agency, Grants ANR-2010-COSI-006 and ANR-2010-BLAN-0904), by the GNR MoMaS (ANDRA, BRGM, CEA, EdF, IRSN, PACEN-CNRS), and by the PRCEU-UCH30/10 grant of the Universidad CEU Cardenal Herrera.
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Falcó, A., Nouy, A. Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces. Numer. Math. 121, 503–530 (2012). https://doi.org/10.1007/s00211-011-0437-5
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DOI: https://doi.org/10.1007/s00211-011-0437-5