Tensor representation of non-linear models using cross approximations

Abstract : Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently , specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor sub-space construction are proposed.
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https://hal.archives-ouvertes.fr/hal-01996047
Contributeur : Jose V. Aguado <>
Soumis le : samedi 16 février 2019 - 10:21:14
Dernière modification le : mardi 28 mai 2019 - 15:40:09
Archivage à long terme le : vendredi 17 mai 2019 - 14:17:31

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Jose Aguado, Domenico Borzacchiello, Kiran Kollepara, Francisco Chinesta, Antonio Huerta. Tensor representation of non-linear models using cross approximations. Journal of Scientific Computing, Springer Verlag, 2019, ⟨10.1007/s10915-019-00917-2⟩. ⟨hal-01996047v2⟩

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