Low Rank Tensor Decompositions and Approximations: Low Rank Tensor Decompositions and Approximations: J. Nie et al.

Jiawang Nie; Li Wang; Zequn Zheng

doi:10.1007/s40305-023-00455-7

Low Rank Tensor Decompositions and Approximations: Low Rank Tensor Decompositions and Approximations: J. Nie et al.

Jiawang Nie^*
, Li Wang
, Zequn Zheng

^*Corresponding author for this work

University of California at San Diego
University of Texas at Arlington

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

1 Citation (Scopus)

Abstract

There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.

Original language	English
Pages (from-to)	847-873
Number of pages	27
Journal	Journal of the Operations Research Society of China
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/s40305-023-00455-7
Publication status	Published - Dec 2024
Externally published	Yes

Keywords

Approximation
Decomposition
Generating polynomial
Rank
Tensor

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Cite this

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abstract = "There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.",

keywords = "Approximation, Decomposition, Generating polynomial, Rank, Tensor",

author = "Jiawang Nie and Li Wang and Zequn Zheng",

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N1 - Publisher Copyright: © The Author(s) 2023.

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N2 - There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.

AB - There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.

KW - Approximation

KW - Decomposition

KW - Generating polynomial

KW - Rank

KW - Tensor

UR - https://www.scopus.com/pages/publications/85150269936

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M3 - Article

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JF - Journal of the Operations Research Society of China

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ER -

Low Rank Tensor Decompositions and Approximations: Low Rank Tensor Decompositions and Approximations: J. Nie et al.

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Keywords

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