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Higher-order QR with tournament pivoting for tensor compression

David Frenkiel 1 Laura Grigori 1 Matthias Beaupère 1
1 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
Abstract : We present in this paper a parallel algorithm that generates a low-rank approximation of a distributed tensor using QR decomposition with tournament pivoting (QRTP). The algorithm, which is a parallel variant of the higher-order singular value decomposition (HOSVD), generates factor matrices for a Tucker decomposition by applying QRTP to the unfolding matrices of a tensor distributed block-wise (by sub-tensor) on a set of processors. For each unfolding mode the algorithm logically reorganizes (unfolds) the processors so that the associated unfolding matrix has a suitable logical distribution. We also establish error bounds between a tensor and the compressed version of the tensor generated by the algorithm.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03079236
Contributor : David Frenkiel <>
Submitted on : Wednesday, December 30, 2020 - 1:18:12 PM
Last modification on : Friday, January 1, 2021 - 3:32:32 AM

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  • HAL Id : hal-03079236, version 4

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David Frenkiel, Laura Grigori, Matthias Beaupère. Higher-order QR with tournament pivoting for tensor compression. 2020. ⟨hal-03079236v4⟩

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