Nonnegative iterations with asymptotically constant coefficients
type: Item
instance of: scholarly article
title: Nonnegative iterations with asymptotically constant coefficients
zbMATH Open document ID: 1176.65045
author: Mihály Pituk
published in: Linear Algebra and its Applications
publication date: 2009-10-09T00:00:00Z
review text: Perron's theory yields a unique (normalized) nonnegative eigenvector for nonnegative matrices. The eigenvalue equals the spectral radius. Now let \(A\) be a matrix that is not necessarily nonnegative, but has the properties above. If the sequence \(A_k\) of matrices converges to \(A\), and \(x_{k+1}=A_k x_k\) is a sequence of nonnegative vectors, and some technical assumptions hold, then \(x_k/\|x_k\|\) converges to the nonnegative eigenvector of \(A\).
reviewed by: D. Braess
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5612557
zbMATH Keywords: nonnegative eigenvectors
zbMATH Keywords: Perron-Frobenius theory
zbMATH Keywords: spectral radius
MaRDI profile type: Publication
full work available at URL: j.laa.2009.06.020
OpenAlex ID: W2077060292
cites work: Q3940059
cites work: Convergence of products of matrices in projective spaces
cites work: Asymptotic Properties for Inhomogeneous Iterations of Nonlinear Operators
cites work: Q5613420
cites work: Q3966611
DOI: 10.1016/J.LAA.2009.06.020
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description: scientific article; zbMATH DE number 5612557