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Adaptive hierarchical subtensor partitioning for tensor compression

Virginie Ehrlacher 1, 2 Laura Grigori 3 Damiano Lombardi 4 Hao Song 3
2 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 COMMEDIA - COmputational Mathematics for bio-MEDIcal Applications
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : In this work a numerical method is proposed to compress a tensor by constructing a piece-wise tensor approximation. This is defined by partitioning a tensor into sub-tensors and by computing a low-rank tensor approximation (in a given format) in each sub-tensor. Neither the partition nor the ranks are fixed a priori, but, instead, are obtained in order to fulfill a prescribed accuracy and optimize, to some extent, the storage. The different steps of the method are detailed and some numerical experiments are proposed to assess its performances.
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Submitted on : Wednesday, September 11, 2019 - 6:19:34 PM
Last modification on : Friday, January 21, 2022 - 3:16:43 AM
Long-term archiving on: : Saturday, February 8, 2020 - 2:10:41 AM

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Virginie Ehrlacher, Laura Grigori, Damiano Lombardi, Hao Song. Adaptive hierarchical subtensor partitioning for tensor compression. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2021, ⟨10.1137/19M128689X⟩. ⟨hal-02284456⟩

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