Revista de la
Unión Matemática Argentina
Some new $Z$-eigenvalue localization sets for tensors and their applications
Zhengge Huang, Ligong Wang, Zhong Xu, and Jingjing Cui
Volume 60, no. 1 (2019), pp. 99–119

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In this paper some new $Z$-eigenvalue localization sets for general tensors are established, which are proved to be tighter than those newly derived by Wang et al. [Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 187–198]. Also, some relationships between the $Z$-eigenvalue inclusion sets presented by Wang et al. and the new $Z$-eigenvalue localization sets for tensors are given. Besides, we discuss the effects of orthonormal transformations for the proposed sets. As applications of the proposed sets, some improved upper bounds for the $Z$-spectral radius of weakly symmetric nonnegative tensors are given. Numerical examples are also given to verify the advantages of our proposed results over some known ones.