Two-step Noda iteration for irreducible nonnegative matrices

In this paper, we present a two-step Noda iteration for computing the Perron root and Perron vector of an irreducible nonnegative matrix by successively solving two linear systems with the same coefficient matrix. For every positive initial vector, the two-step Noda iteration always converges and ha...

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Published inLinear & multilinear algebra Vol. 72; no. 3; pp. 367 - 378
Main Authors Shan Chen, Xiao, Hao Ou, Li
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 11.02.2024
Taylor & Francis Ltd
Subjects
Convergence
cubic convergence
irreducible nonnegative matrix
Iterative methods
Linear systems
M-matrix
Mathematical analysis
Matrices (mathematics)
Two-step Noda iteration
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Summary:In this paper, we present a two-step Noda iteration for computing the Perron root and Perron vector of an irreducible nonnegative matrix by successively solving two linear systems with the same coefficient matrix. For every positive initial vector, the two-step Noda iteration always converges and has a cubic asymptotic convergence rate. As an application, the two-step Noda iteration is applied to compute the smallest eigenpair of irreducible nonsingular M-matrices. Numerical examples are provided for testing the proposed method.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2022.2158298