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Noda iterations for generalized eigenproblems following Perron-Frobenius theory
Xiao Shan Chen1; Seak-Weng Vong2; Wen Li1; Hongguo Xu3
2019-03
Source PublicationNumerical Algorithms
ISSN1017-1398
Volume80Issue:3Pages:937–955
Abstract

In this paper, we investigate the generalized eigenvalue problem Ax = λBx arising from economic models. Under certain conditions, there is a simple generalized eigenvalue ρ(A, B) in the interval (0, 1) with a positive eigenvector. Based on the Noda iteration, a modified Noda iteration (MNI) and a generalized Noda iteration (GNI) are proposed for finding the generalized eigenvalue ρ(A, B) and the associated unit positive eigenvector. It is proved that the GNI method always converges and has a quadratic asymptotic convergence rate. So GNI has a similar convergence behavior as MNI. The efficiency of these algorithms is illustrated by numerical examples.

KeywordGeneralized Eigenproblem Generalized Noda Iteration Nonnegative Irreducible Matrix M-matrix Quadratic Convergence Perron-frobenius Theory
DOIhttps://doi.org/10.1007/s11075-018-0512-4
Language英语
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Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorXiao Shan Chen; Seak-Weng Vong; Wen Li; Hongguo Xu
Affiliation1.School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China
2.Department of Mathematics, University of Macau, Macau, China
3.Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Xiao Shan Chen,Seak-Weng Vong,Wen Li,et al. Noda iterations for generalized eigenproblems following Perron-Frobenius theory[J]. Numerical Algorithms,2019,80(3):937–955.
APA Xiao Shan Chen,Seak-Weng Vong,Wen Li,&Hongguo Xu.(2019).Noda iterations for generalized eigenproblems following Perron-Frobenius theory.Numerical Algorithms,80(3),937–955.
MLA Xiao Shan Chen,et al."Noda iterations for generalized eigenproblems following Perron-Frobenius theory".Numerical Algorithms 80.3(2019):937–955.
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