Abstract
A lower boundn −1Σ i,k aik for the Perron eigenvalue of a symmetric non-negative irreducible matrixA=(a ik) is studied and compared with certain other lower bounds.
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References
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.
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.
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.
A. Ostrowski and H. Schneider,Bounds for the maximal characteristic root of a non-negative irreducible matrix, Duke Math. J. 27 (1960), 547–553.
J. H. Wilkinson,Householder's method for symmetric matrices, Numer. Math. 4 (1962), 354–361.
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Merikoski, J.K. On a lower bound for the perron eigenvalue. BIT 19, 39–42 (1979). https://doi.org/10.1007/BF01931220
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DOI: https://doi.org/10.1007/BF01931220