Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix
type: Item
instance of: scholarly article
title: Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix
zbMATH Open document ID: 0627.65035
DOI: 10.1016/0024-3795(87)90158-3
author: Moshe Haviv
author: Yaacov Ritov
author: Uriel G. Rothblum
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4020323
zbMATH Keywords: irreducible nonnegative square matrix
zbMATH Keywords: spectral radius
zbMATH Keywords: positive eigenvector
zbMATH Keywords: subdominant modulus of an eigenvalue
zbMATH Keywords: convergence
zbMATH Keywords: sequence of bounds
reviewed by: Waldemar Velte
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90158-3
OpenAlex ID: W1980710169
cites work: Q3943082
cites work: A remark on the paper of H. H. Schaefer 'Abschätzung der nichttrivialen Eigenwerte stochastischer Matrizen'
cites work: Three observations on nonnegative matrices
cites work: Q5526485
cites work: Q3909515
cites work: Upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices
cites work: Non-negative matrices and Markov chains. 2nd ed
description: scientific article; zbMATH DE number 4020323