【摘 要】
：
The sub-dominant eigenvalue of a stochastic matrix affects the convergence behav-ior of a Markov chain. L.J. Cvetkovi et al. (SIAM J. Matrix Anal. Appl., 32
【出 处】
：
2016年张量和矩阵学术研讨会(International conference on Tensor, Matrix a
论文部分内容阅读
The sub-dominant eigenvalue of a stochastic matrix affects the convergence behav-ior of a Markov chain. L.J. Cvetkovi et al. (SIAM J. Matrix Anal. Appl., 32 (2011) 771784 ) and Shen et al. (Linear Algebra and its Applications, 447(2014) 7487) mod-ified respectively the Gergorin circle set to localize all eigenvalues different from 1 for stochastic matrices by 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. To conquer this drawback, we introduce some new modifications of the Gergorin circle set to capture all eigenvalues different from 1 more precisely. The modification problem for Brauer Cassini ovals is also discussed. Lastly, we present some questions on the sub-dominant eigenvalue of a transition probability tensor.
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