Some improved Ky Fan type eigenvalue inclusion sets for tensors
Computing eigenvalues of a tensor is not easy when its order and dimension are large. One way to deal with the challenge is to find inclusion sets for the eigenvalues. Motivated by the work of \textit{K. Fan} [Duke Math. J. 25, 441--445 (1958; Zbl 0081.25202)] on eigenvalue inclusion set for matrices, \textit{Y. Yang} and \textit{Q. Yang} [SIAM J. Matrix Anal. Appl. 31, No. 5, 2517--2530 (2010; Zbl 1227.15014)] extended the Fan's result to tensors. \textit{J. He} and \textit{T.-Z. Huang} [J. Inequal. Appl. 2014, Paper No. 114, 9 p. (2014; Zbl 1372.15006)] obtained inclusion sets for the eigenvalues of a tensor via the theory of strong \(\mathcal M\)-tensors. This paper presents two classes of new Fan-type eigenvalue inclusion sets for tensors, which are tighter than those mentioned above. Under some conditions, the theoretical comparisons of the new proposed Fan-type eigenvalue inclusion sets are established and numerical examples are given.
scientific article; zbMATH DE number 7347037
scientific article