New localization theorems for the M-eigenvalues of a fourth-order partially symmetric tensor

M-eigenvalues of a fourth-order partially symmetric tensor have extensive research and applications in nonlinear elastic material analysis and quantum physics, which promotes the development of the M-eigenvalue estimating problems for fourth-order partially symmetric tensors. In this paper, we propose some new localization sets to investigate the distribution of the M-eigenvalues for a fourth-order partially symmetric tensor, which improves some existing ones in [Li et al., M-eigenvalue inclusion intervals for a fourth-order partially symmetric tensor, J. Comput. Appl. Math., 365 (2019) 391-401]. Using newly proposed M-eigenvalue localization sets, some new upper bounds on the M-spectral radius of fourth-order partially symmetric nonnegative tensors which are better than some existing ones are obtained. Finally, some numerical experiments are performed to show the effectiveness of our main results.