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Numerische Mathematik

, Volume 19, Issue 3, pp 209–211 | Cite as

A comparison of some bounds for the nontrivial eigenvalues of stochastic matrices

  • Christoph Zenger
Article

Summary

Some recently published bounds for the nontrivial eigenvalues of stochastic matrices [1, 2, 4, 5] are compared. It is shown that the Deutsch bound [1] is the best of these bounds and is only slightly improved by a bound given in [3].

Keywords

Mathematical Method Stochastic Matrice Nontrivial Eigenvalue 
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References

  1. 1.
    Bauer, F. L., Deutsch, E., Stoer, J.: Abschätzungen für die Eigenwerte positiver linearer Operatoren. Lin. Alg. Appl.2, 275–301 (1969).Google Scholar
  2. 2.
    Brauer, A.: A remark on the paper of H. H. Schaefer: Abschätzung der nichttrivialen Eigenwerte stochastischer Matrizen. Num. Math.17, 163–165 (1971).Google Scholar
  3. 3.
    Deutsch, E., Zenger, Chr.: Inclusion domains for the eigenvalues of stochastic matrices. Num. Math.18, 182–192 (1971).Google Scholar
  4. 4.
    Hadeler, K. P.: Abschätzungen für den zweiten Eigenwert eines positiven Operators. Aequationes Math.5, 227–235 (1970).Google Scholar
  5. 5.
    Schaefer, H. H.: Eine Abschätzung der nichttrivialen Eigenwerte stochastischer Matrizen. Num. Math.15, 219–223 (1970).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Christoph Zenger
    • 1
  1. 1.Leibniz-Rechenzentrum der Bayerischen Akademie der WissenschaftenMünchen 2Germany

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