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Article Dans Une Revue Numerische Mathematik Année : 2012

Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces

Résumé

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 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 Proper Generalized Decompositions for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banach space.

Dates et versions

hal-00609108 , version 1 (18-07-2011)

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Antonio Falco, Anthony Nouy. Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces. Numerische Mathematik, 2012, 121 (3), pp.503-530. ⟨10.1007/s00211-011-0437-5⟩. ⟨hal-00609108⟩
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