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Tensor Representation of Non-linear Models Using Cross Approximations

Article dans une revue avec comité de lecture
Author
AGUADO, Jose Vicente
111023 École Centrale de Nantes [ECN]
BORZACCHIELLO, Domenico
111023 École Centrale de Nantes [ECN]
KOLLEPARA, Kiran S.
111023 École Centrale de Nantes [ECN]
HUERTA, Antonio
85878 Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona] [UPC]
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/17719
DOI
10.1007/s10915-019-00917-2
Date
2019
Journal
Journal of Scientific Computing

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 subspace construction are proposed.

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