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

^*此作品的通讯作者

University of California at San Diego
University of Texas at Arlington

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	847-873
页数	27
期刊	Journal of the Operations Research Society of China
卷	12
期	4
DOI	https://doi.org/10.1007/s40305-023-00455-7
出版状态	已出版 - 12月 2024
已对外发布	是

访问文件

10.1007/s40305-023-00455-7

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{c2f27e5de8764eafb9a861bbe4718553,

title = "Low Rank Tensor Decompositions and Approximations: Low Rank Tensor Decompositions and Approximations: J. Nie et al.",

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",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2023.",

year = "2024",

month = dec,

doi = "10.1007/s40305-023-00455-7",

language = "English",

volume = "12",

pages = "847--873",

journal = "Journal of the Operations Research Society of China",

issn = "2194-668X",

publisher = "Springer International Publishing",

number = "4",

}

TY - JOUR

T1 - Low Rank Tensor Decompositions and Approximations

T2 - Low Rank Tensor Decompositions and Approximations: J. Nie et al.

AU - Nie, Jiawang

AU - Wang, Li

AU - Zheng, Zequn

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

PY - 2024/12

Y1 - 2024/12

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

U2 - 10.1007/s40305-023-00455-7

DO - 10.1007/s40305-023-00455-7

M3 - Article

AN - SCOPUS:85150269936

SN - 2194-668X

VL - 12

SP - 847

EP - 873

JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

IS - 4

ER -

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

摘要

访问文件

其它文件与链接

学术指纹

引用此