Finding the largest eigenvalue of a nonnegative tensor

Michael Ng; Liqun Qi; Guanglu Zhou

doi:10.1137/09074838X

Finding the largest eigenvalue of a nonnegative tensor

Michael Ng, Liqun Qi, Guanglu Zhou

Research output: Journal article publication › Journal article › Academic research › peer-review

230 Citations (Scopus)

Abstract

In this paper we propose an iterative method for calculating the largest eigenvalue of an irreducible nonnegative tensor. This method is an extension of a method of Collatz (1942) for calculating the spectral radius of an irreducible nonnegative matrix. Numerical results show that our proposed method is promising. We also apply the method to studying higher-order Markov chains.

Original language	English
Pages (from-to)	1090-1099
Number of pages	10
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	31
Issue number	3
DOIs	https://doi.org/10.1137/09074838X
Publication status	Published - 28 Dec 2009

Keywords

Higher-order markov chains
Iterative method
Nonnegative tensor
Spectral radius

ASJC Scopus subject areas

Analysis

More information

10.1137/09074838X

http://hdl.handle.net/10397/6109

Cite this

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AB - In this paper we propose an iterative method for calculating the largest eigenvalue of an irreducible nonnegative tensor. This method is an extension of a method of Collatz (1942) for calculating the spectral radius of an irreducible nonnegative matrix. Numerical results show that our proposed method is promising. We also apply the method to studying higher-order Markov chains.

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KW - Spectral radius

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DO - 10.1137/09074838X

M3 - Journal article

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JF - SIAM Journal on Matrix Analysis and Applications

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Finding the largest eigenvalue of a nonnegative tensor

Abstract

Keywords

ASJC Scopus subject areas

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