title: A newS-type eigenvalue inclusion set for tensors and its applications.
abstract: In this paper, a newS-type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsetsSand its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Liet al.(Numer. Linear Algebra Appl. 21:39-50, 2014) and Liet al.(Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimumH-eigenvalue of strongM-tensors are established, and we prove that these bounds are tighter than those obtained by Liet al.(Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014).
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
authors.forename: Zheng-Ge
authors.initials: ZG
authors.lastname: Huang
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
authors.forename: Li-Gong
authors.initials: LG
authors.lastname: Wang
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
authors.forename: Zhong
authors.initials: Z
authors.lastname: Xu
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
authors.forename: Jing-Jing
authors.initials: JJ
authors.lastname: Cui
keywords: minimum H-eigenvalue; nonnegative tensor; nonsingular M-tensor; positive definite; spectral radius; tensor eigenvalue