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A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices AbstractA set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014) 74-87) and Li et al. (Linear and Multilinear Algebra 63(11) (2015) 2159-2170) for estimating the moduli of subdominant eigenvalues. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

Wang, Xiaoxiao; Li, Chaoqian; Li, Yaotang
Open Mathematics , Volume 16 (1): 13 – Apr 2, 2018
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Publisher
de Gruyter
Copyright
© 2018 Wang et al., published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0030
Publisher site
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Abstract

AbstractA set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014) 74-87) and Li et al. (Linear and Multilinear Algebra 63(11) (2015) 2159-2170) for estimating the moduli of subdominant eigenvalues.

Journal

Open Mathematics – de Gruyter

Published: Apr 2, 2018

Keywords: Stochastic Matrix; Geršgorin set; Subdominant eigenvalue; 65F15; 15A18; 15A51

References

  • Geršgorin-type and Brauer-type eigenvalue localization sets of stochastic matrices
  • Subdominant eigenvalues for stochastic matrices with given column sums
  • Stochastic Markov models of the formation and disintegration of binary complexes
  • A characterization of birth and death processes
  • A modification of eigenvalue localization for stochastic matrices
  • Sensitivity and convergence of uniformly ergodic Markov chains
  • Eigenvalue Localization Refinements for Matrices Related to Positivity