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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 = {Wen Li, Weihui Liu and Seakweng Vong}, 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 AU - Wen Li, Weihui Liu & Seakweng Vong 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 and Seakweng Vong. (2018). 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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