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Volume 11, Issue 4
On the Z-Eigenvalue Bounds for a Tensor

Wen Li, Weihui Liu & Seakweng Vong

DOI: 10.4208/nmtma.2018.s08

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 810-826.

Published online: 2018-06

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  • Abstract

In this paper, we first propose a $Z_p$-eigenvalue of a tensor, which includes the $Z_1$- and $Z_2$-eigenvalue as its special case, and then present a $Z_p$-eigenvalue bound. In particular, we give a $Z$-spectral radius bound for an irreducible nonnegative tensor via the spectral radius of a nonnegative matrix. The proposed bounds improve some existing ones. Some numerical examples are given to show the validity of the proposed bounds.

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@Article{NMTMA-11-810, author = {}, title = {On the Z-Eigenvalue Bounds for a Tensor}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {4}, pages = {810--826}, abstract = {

In this paper, we first propose a $Z_p$-eigenvalue of a tensor, which includes the $Z_1$- and $Z_2$-eigenvalue as its special case, and then present a $Z_p$-eigenvalue bound. In particular, we give a $Z$-spectral radius bound for an irreducible nonnegative tensor via the spectral radius of a nonnegative matrix. The proposed bounds improve some existing ones. Some numerical examples are given to show the validity of the proposed bounds.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2018.s08}, url = {http://global-sci.org/intro/article_detail/nmtma/12474.html} }
TY - JOUR T1 - On the Z-Eigenvalue Bounds for a Tensor JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 810 EP - 826 PY - 2018 DA - 2018/06 SN - 11 DO - http://doi.org/10.4208/nmtma.2018.s08 UR - https://global-sci.org/intro/article_detail/nmtma/12474.html KW - AB -

In this paper, we first propose a $Z_p$-eigenvalue of a tensor, which includes the $Z_1$- and $Z_2$-eigenvalue as its special case, and then present a $Z_p$-eigenvalue bound. In particular, we give a $Z$-spectral radius bound for an irreducible nonnegative tensor via the spectral radius of a nonnegative matrix. The proposed bounds improve some existing ones. Some numerical examples are given to show the validity of the proposed bounds.

Wen Li, Weihui Liu & Seakweng Vong. (2020). On the Z-Eigenvalue Bounds for a Tensor. Numerical Mathematics: Theory, Methods and Applications. 11 (4). 810-826. doi:10.4208/nmtma.2018.s08
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