New estimations on the upper bounds for the nuclear norm of a tensor

Xu Kong; Jicheng Li; Xiaolong Wang

doi:10.1186/s13660-018-1861-1

New estimations on the upper bounds for the nuclear norm of a tensor

Xu Kong
, Jicheng Li
, Xiaolong Wang

School of Mathematics and Statistics

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

1 Scopus citations

Abstract

Using the orthogonal rank of the tensor, a new estimation method for the upper bounds on the nuclear norms is presented and some new tight upper bounds on the nuclear norms are established. Taking into account the structure information of the tensor, an important factor affecting the upper bounds is discussed and some corresponding properties related to the nuclear norms are given. Meanwhile, some new results of the upper bounds on the nuclear norms are obtained.

Original language	English
Article number	282
Journal	Journal of Inequalities and Applications
Volume	2018
DOIs	https://doi.org/10.1186/s13660-018-1861-1
State	Published - 2018

Keywords

Nuclear norm
Orthogonal rank
Tensor
Upper bound

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10.1186/s13660-018-1861-1

Cite this

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title = "New estimations on the upper bounds for the nuclear norm of a tensor",

abstract = "Using the orthogonal rank of the tensor, a new estimation method for the upper bounds on the nuclear norms is presented and some new tight upper bounds on the nuclear norms are established. Taking into account the structure information of the tensor, an important factor affecting the upper bounds is discussed and some corresponding properties related to the nuclear norms are given. Meanwhile, some new results of the upper bounds on the nuclear norms are obtained.",

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author = "Xu Kong and Jicheng Li and Xiaolong Wang",

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year = "2018",

doi = "10.1186/s13660-018-1861-1",

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AU - Kong, Xu

AU - Li, Jicheng

AU - Wang, Xiaolong

PY - 2018

Y1 - 2018

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AB - Using the orthogonal rank of the tensor, a new estimation method for the upper bounds on the nuclear norms is presented and some new tight upper bounds on the nuclear norms are established. Taking into account the structure information of the tensor, an important factor affecting the upper bounds is discussed and some corresponding properties related to the nuclear norms are given. Meanwhile, some new results of the upper bounds on the nuclear norms are obtained.

KW - Nuclear norm

KW - Orthogonal rank

KW - Tensor

KW - Upper bound

UR - https://www.scopus.com/pages/publications/85054781295

U2 - 10.1186/s13660-018-1861-1

DO - 10.1186/s13660-018-1861-1

M3 - 文章

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SN - 1025-5834

VL - 2018

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

M1 - 282

ER -

New estimations on the upper bounds for the nuclear norm of a tensor

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Keywords

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