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

被引：0

作者：

Che, Maolin ^{[1
]}

Wei, Yimin ^{[2
,3
]}

Xu, Yanwei ^{[4
]}

机构：

[1] Southwestern Univ Finance & Econ, Sch Math, Chengdu 611130, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Fudan Univ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

[4] Huawei Technol Co Ltd, Theory Lab, Cent Res Inst, 2012 Labs, Hong Kong, Peoples R China

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2023年 / 87卷 / 2-4期

关键词：

Randomized algorithms; Random projection; Multilinear rank-(mu(1); mu(2); mu(3)); approximation; Sparse subspace embedding; Singular value decomposition; Singular values; The power scheme; TENSOR; TUCKER; MATRIX; DECOMPOSITION;

D O I：

10.1007/s10898-022-01182-8

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We present some randomized algorithms for computing multilinear rank-(mu(1),mu(2),mu(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.

引用

页码：373 / 403

页数：31

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