×

Ergodicity coefficients defined by vector norms. (English) Zbl 1223.15043

Ergodicity coefficients for stochastic matrices determine inclusion regions for subdominant eigenvalues; estimate the sensitivity of the stationary distribution to changes in the matrix; and bound the convergence rate of methods for computing the stationary distribution. Before the present paper, there have been many scattered results on ergodicity coefficients and the relations among them are not very clear. In this paper, the authors present a coherent discussion of existing results, with simplified and complete proofs. The authors also deduce some new results on ergodicity coefficients defined by \(p\)-norms, not only for stochastic matrices but also for general real and complex matrices.

MSC:

15B51 Stochastic matrices
15A18 Eigenvalues, singular values, and eigenvectors
15A42 Inequalities involving eigenvalues and eigenvectors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
PDFBibTeX XMLCite
Full Text: DOI Link