Positive eigenvector of nonlinear perturbations of nonsymmetric \(M\)-matrix and Newton iterative solution
type: Item
instance of: scholarly article
title: Positive eigenvector of nonlinear perturbations of nonsymmetric \(M\)-matrix and Newton iterative solution
zbMATH Open document ID: 1154.65019
author: Shi-Liang Wu
author: Da-Ping Liu
author: Yaotang Li
published in: Applied Mathematics and Computation
publication date: 2008-06-17T00:00:00Z
review text: This paper concerns nonlinear perturbations of nonsymmetric \(M\)-matrices and their Newton iterative solutions, as needed in modeling the Bose-Einstein condensation of matter at near absolute zero temperatures. It is shown that any number greater than the smallest positive eigenvalue of the \(M\)-matrix is an eigenvalue of the nonlinear problem and that the corresponding positive eigenvector is unique and the Newton iteration of the positive eigenvector is convergent. Moreover, such positive eigenvectors form a monotone increasing and continuous function of the corresponding eigenvalues.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5289106
zbMATH Keywords: \(M\)-matrix
zbMATH Keywords: nonlinear perturbation
zbMATH Keywords: eigenvalue
zbMATH Keywords: Newton iterative solution
zbMATH Keywords: Bose-Einstein condensation of matter
zbMATH Keywords: positive eigenvector
reviewed by: Erwin O. Kreyszig
MaRDI profile type: Publication
full work available at URL: j.amc.2007.11.008
OpenAlex ID: W2078286802
cites work: A generalization of the Perron-Frobenius theorem for nonlinear perturbations of Stieltjes matrices
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DOI: 10.1016/J.AMC.2007.11.008
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description: scientific article; zbMATH DE number 5289106