Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces

Antonio Falco; Anthony Nouy

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arXiv · 1106.4424

Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces

Antonio Falco·Anthony Nouy

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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 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.

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Antonio Falco, Anthony Nouy. 2011-06-22. Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces. https://arxiv.org/abs/1106.4424

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