Rank-one approximation to high order tensors

Tong Zhang; Gene H. Golub

doi:10.1137/S0895479899352045

Rank-one approximation to high order tensors

Tong Zhang^*, Gene H. Golub

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

350 Citations (Scopus)

Abstract

The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211-218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.

Original language	English
Pages (from-to)	534-550
Number of pages	17
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	23
Issue number	2
DOIs	https://doi.org/10.1137/S0895479899352045
Publication status	Published - 2002
Externally published	Yes

Keywords

Low-rank approximation
Singular value decomposition
Tensor decomposition

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10.1137/S0895479899352045

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abstract = "The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211-218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.",

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AU - Golub, Gene H.

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AB - The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211-218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.

KW - Low-rank approximation

KW - Singular value decomposition

KW - Tensor decomposition

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000172891000015

UR - https://openalex.org/W2002598080

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DO - 10.1137/S0895479899352045

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SP - 534

EP - 550

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 2

ER -

Rank-one approximation to high order tensors

Abstract

Keywords

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