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

Abstract

Abstract In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing N = { 1 , 2 , … , n } $N=\{1,2,\ldots,n\}$ into disjoint subsets S 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 et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and Li et al. (Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimum H-eigenvalue of strong M-tensors are established, and we prove that these bounds are tighter than those obtained by Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014).

Keywords

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