Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix (Q1092608)

Considered is an irreducible nonnegative square matrix B where, by assumption, the spectral radius \(\rho\) (B) and a corresponding positive eigenvector w are known. In terms of \(\rho\) (B) and w, two easily computable sequences of bounds on the subdominant modulus of an eigenvalue are introduced, and their convergence to the subdominant modulus are shown. A sequence of bounds generated by a method of \textit{A. Brauer} [Numer. Math. 17, 163-165 (1971; Zbl 0206.464)] turns out to be a subsequence of one of the two sequences under consideration. Thus, the results presented imply the convergence of Brauer's sequence.