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A simple method for estimating the bounds of spectral radius of nonnegative irreducible matrices. (English) Zbl 1227.05278

Summary: Based on the Perron complement \(P(A/A[\alpha])\) and generalized Perron complement \(P_t(A/A[\alpha])\) of a nonnegative irreducible matrix \(A\), we derive a simple and practical method that estimates the upper and lower bounds of the spectral radius of \(A\) in terms of norms of \(A[\alpha]\) and its complements. Numerical examples show that this approach improves some of the classical estimates.

MSC:

05E99 Algebraic combinatorics
15A18 Eigenvalues, singular values, and eigenvectors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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