Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/93825
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Qi, L | en_US |
dc.creator | Hu, S | en_US |
dc.creator | Xu, Y | en_US |
dc.date.accessioned | 2022-08-01T06:00:22Z | - |
dc.date.available | 2022-08-01T06:00:22Z | - |
dc.identifier.issn | 1553-166X | en_US |
dc.identifier.uri | http://hdl.handle.net/10397/93825 | - |
dc.language.iso | en | en_US |
dc.publisher | American Institute of Mathematical Sciences | en_US |
dc.rights | © 2021 The Author(s). Published by AIMS, LLC. This is an Open Access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). | en_US |
dc.rights | The following publication Liqun Qi, Shenglong Hu, Yanwei Xu. Spectral norm and nuclear norm of a third order tensor. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1101-1113 is available at https://doi.org/10.3934/jimo.2021010. | en_US |
dc.subject | Biquadratic tensor | en_US |
dc.subject | Nuclear norm | en_US |
dc.subject | Spectral norm | en_US |
dc.subject | Third order tensor | en_US |
dc.title | Spectral norm and nuclear norm of a third order tensor | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 1101 | en_US |
dc.identifier.epage | 1113 | en_US |
dc.identifier.volume | 18 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.doi | 10.3934/jimo.2021010 | en_US |
dcterms.abstract | The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order tensor is equal to the square root of the spectral norm of three positive semi-definite biquadratic tensors, and the square roots of the nuclear norms of those three positive semi-definite biquadratic tensors are lower bounds of the nuclear norm of that third order tensor. This provides a way to estimate and to evaluate the spectral norm and the nuclear norm of that third order tensor. Some upper and lower bounds for the spectral norm and nuclear norm of a third order tensor, by spectral radii and nuclear norms of some symmetric matrices, are presented. | en_US |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | Journal of industrial and management optimization, Mar 2022, v. 18, no. 2, p. 1101-1113 | en_US |
dcterms.isPartOf | Journal of industrial and management optimization | en_US |
dcterms.issued | 2022-03 | - |
dc.identifier.scopus | 2-s2.0-85099764437 | - |
dc.identifier.eissn | 1547-5816 | en_US |
dc.description.validate | 202208_bcww | en_US |
dc.description.oa | Version of Record | en_US |
dc.identifier.FolderNumber | OA_Others | - |
dc.description.pubStatus | Published | en_US |
dc.description.TA | AIMS (2022) | en_US |
dc.description.oaCategory | TA | en_US |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
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Qi_Spectral_Norm_Nuclear.pdf | 307.74 kB | Adobe PDF | View/Open |
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