Geršgorin-type and Brauer-type eigenvalue localization sets of stochastic matrices
Chaoqian Li, Qingbing Liu, Yaotang Li · Linear and Multilinear Algebra · 2014
Shen et al. in [Some classes of nonsingular matrices with applications to localize the real eigenvalues of real matrices, Linear Algebra and its Applications, 447 (2014), pp. 74–87] modified the Geršgorin circle set to localize all eigenvalues different from for stochastic matrices using the least off-diagonal element of each column. However, the modification does not always work when the least off-diagonal element of each column is 0. In this paper, we provide new methods to modify the Geršgorin and Brauer eigenvalue localization set. And numerical examples are given to show that new eigenvalue localization sets capture all eigenvalues different from for stochastic matrices more precisely than those provided by Shen et al.