Randomized algorithms for the computation of multilinear rank- $$(\mu _1,\mu _2,\mu _3)$$ ( μ 1, μ 2, μ 3 ) approximations

Maolin Che (), Yimin Wei () and Yanwei Xu ()
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Maolin Che: Southwestern University of Finance and Economics
Yimin Wei: Fudan University
Yanwei Xu: Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co., Ltd.

Journal of Global Optimization, 2023, vol. 87, issue 2, No 4, 373-403

Abstract: Abstract We present some randomized algorithms for computing multilinear rank- $$(\mu _1,\mu _2,\mu _3)$$ ( 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.

Keywords: Randomized algorithms; Random projection; Multilinear rank- $$(\mu _1{; }\mu _2{; }\mu _3)$$ ( μ 1; μ 2; μ 3 ) approximation; Sparse subspace embedding; Singular value decomposition; Singular values; The power scheme; 15A18; 65F15; 65F10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01182-8

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