A new -type eigenvalue inclusion set for tensors and its applications.

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Zheng-Ge Huang, Li-Gong Wang, Zhong Xu, Jing-Jing Cui

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Zheng-Ge Huang: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
Li-Gong Wang: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
Zhong Xu: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
Jing-Jing Cui: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.

PMID: 28077920 DOI: 10.1186/s13660-016-1200-3

In this paper, a new -type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsets and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Li (Numer. Linear Algebra Appl. 21:39-50, 2014) and Li (Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimum -eigenvalue of strong -tensors are established, and we prove that these bounds are tighter than those obtained by Li (Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014).

minimum H-eigenvalue nonnegative tensor nonsingular M-tensor positive definite spectral radius tensor eigenvalue

J Inequal Appl. 2017;2017(1):88 [PMID: 28503057]

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