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http://hdl.handle.net/10397/93825
Title: | Spectral norm and nuclear norm of a third order tensor | Authors: | Qi, L Hu, S Xu, Y |
Issue Date: | Mar-2022 | Source: | Journal of industrial and management optimization, Mar 2022, v. 18, no. 2, p. 1101-1113 | 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. | Keywords: | Biquadratic tensor Nuclear norm Spectral norm Third order tensor |
Publisher: | American Institute of Mathematical Sciences | Journal: | Journal of industrial and management optimization | ISSN: | 1553-166X | EISSN: | 1547-5816 | DOI: | 10.3934/jimo.2021010 | 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/). 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. |
Appears in Collections: | Journal/Magazine Article |
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