BIT Numerical Mathematics

, Volume 19, Issue 1, pp 39–42 | Cite as

On a lower bound for the perron eigenvalue

  • Jorma Kaarlo Merikoski
Article

Abstract

A lower boundn−1Σ i,k aik for the Perron eigenvalue of a symmetric non-negative irreducible matrixA=(aik) is studied and compared with certain other lower bounds.

Keywords

Lower Bound Computational Mathematic Irreducible matrixA Perron Eigenvalue 

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References

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    A. Brauer and I. C. Gentry,Bounds for the greatest characteristic root of an irreducible non-negative matrix, Lin. Alg. Appl. 8 (1974), 105–107.Google Scholar
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    R. A. Brooker and F. H. Sumner,The method of Lanczos for calculating the characteristic roots and vectors of a real symmetric matrix, Proc. I.E.E. 103 (1956) Part B, Suppl. 1, 114.Google Scholar
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    C. A. Hall and T. A. Porsching,Bounds for the maximal eigenvalue of a non-negative irreducible matrix, Duke Math. J. 36 (1969), 159–164.Google Scholar
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    A. Ostrowski and H. Schneider,Bounds for the maximal characteristic root of a non-negative irreducible matrix, Duke Math. J. 27 (1960), 547–553.Google Scholar
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    J. H. Wilkinson,Householder's method for symmetric matrices, Numer. Math. 4 (1962), 354–361.Google Scholar

Copyright information

© BIT Foundations 1979

Authors and Affiliations

  • Jorma Kaarlo Merikoski
    • 1
  1. 1.Department of Mathematical SciencesUniversity of TampereTampere 10Finland

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