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Preprints, Working Papers, ... Year : 2022

Higher-order QR with tournament pivoting for tensor compression

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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Dates and versions

hal-03079236 , version 1 (17-12-2020)
hal-03079236 , version 2 (17-12-2020)
hal-03079236 , version 3 (18-12-2020)
hal-03079236 , version 4 (30-12-2020)
hal-03079236 , version 5 (02-02-2022)

Identifiers

  • HAL Id : hal-03079236 , version 5

Cite

David Frenkiel, Laura Grigori, Matthias Beaupère. Higher-order QR with tournament pivoting for tensor compression. 2022. ⟨hal-03079236v5⟩
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