Some inequalities on the Perron eigenvalue and eigenvectors for positive tensors (Q2790781)

About ten years ago, \textit{L. Qi} [J. Symb. Comput. 40, No. 6, 1302--1324 (2005; Zbl 1125.15014)] and \textit{L. H. Lim} [``Singular values and eigenvalues of tensors: a variational approach'', in: Proceedings of the 1st IEEE international workshop on computational advances of multitensor adative processing. Piscataway, NJ: IEEE. 129--132 (2005; \url{doi:10.1109/CAMAP.2005.1574201})] independently introduced the notion of eigenvalue problems for symmetric tensors. Using a technique of \textit{A. M. Ostrowski} [Proc. Edinb. Math. Soc., II. Ser. 12, 107--112 (1960; Zbl 0102.01501)] and \textit{H. Schneider} [Proc. Edinb. Math. Soc., II. Ser. 11, 127--130 (1958; Zbl 0085.01104)], the authors establish new bounds for the maximal eigenvalue and eigenvector of positive tensors and show that the bounds are sharper than those of \textit{Z. Wang} and \textit{W. Wu} [J. Ind. Manag. Optim. 10, No. 4, 1031--1039 (2014; Zbl 1292.15010)]. A numerical example is given.