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

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

267 Citations (Scopus)

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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
Early online date	28 Aug 2009
DOIs	https://doi.org/10.1137/09074838X
Publication status	Published - May 2010

Scopus Subject Areas

Analysis

User-Defined Keywords

Higher-order markov chains
Iterative method
Nonnegative tensor
Spectral radius

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title = "Finding the Largest Eigenvalue of a Nonnegative Tensor",

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.",

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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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Finding the Largest Eigenvalue of a Nonnegative Tensor

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