Topic: Perron vector analysis for irreducible nonnegative tensors and its applications
Speaker: Professor Li Wen
Event date: 5/18/2019
Event time: 16:00 p.m.
Venue: Lecture Hall 204, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract:
The ratio of the entries of the Perron vector of an irreducible nonnegative matrix can be applied to the dynamics of digital circuits. In this talk, we present some lower and upper bounds for the ratio of the smallest and largest entries of a Perron vector for an irreducible nonnegative tensor with new techniques, which always improve the existing ones. Applying these new ratio results, we first refine two-sided bounds for the spectral radius of an irreducible nonnegative tensor. In particular, for the matrix case, the new bounds also improve the corresponding ones. Second, we provide a new Ky Fan type theorem, which improves the existing one. Third, we refine the perturbation bound for the spectral radii of nonnegative tensors, from which one may derive a comparison theorem for spectral radii of nonnegative tensors. Numerical examples are given to show the efficiency of the theoretical results.