Randomized algorithms for the computation of multilinear rank-(μ1,μ2,μ3) approximations

We present some randomized algorithms for computing multilinear rank- ( μ 1 , μ 2 , μ 3 ) approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse su...

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Bibliographic Details
Published in:Journal of global optimization Vol. 87; no. 2-4; pp. 373 - 403
Main Authors: Che, Maolin, Wei, Yimin, Xu, Yanwei
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2023
Springer
Subjects:
Algorithms
Analysis
Computer Science
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
approximation
Multilinear rank
65F10
Singular values
Randomized algorithms
Sparse subspace embedding
65F15
Random projection
The power scheme
Singular value decomposition
15A18
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We present some randomized algorithms for computing multilinear rank- ( μ 1 , μ 2 , μ 3 ) approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse subspace embedding. Furthermore, combining the power scheme and the proposed randomized algorithm, we derive a three-stage randomized algorithm and make a probabilistic analysis for its error bound. The efficiency of the proposed algorithms is illustrated via numerical examples.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01182-8