Finding the Largest Eigenvalue of a Nonnegative Tensor

Authors:
Michael Ng;Liqun Qi;Guanglu Zhou
Affiliations:
mng@math.hkbu.edu.hk;maqilq@polyu.edu.hk;G.Zhou@curtin.edu.au
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2009

Citing 0
Cited 6

An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor

Journal of Computational and Applied Mathematics
Foreword

Computational Optimization and Applications
Further Results for Perron-Frobenius Theorem for Nonnegative Tensors

SIAM Journal on Matrix Analysis and Applications
Further Results for Perron-Frobenius Theorem for Nonnegative Tensors II

SIAM Journal on Matrix Analysis and Applications
On determinants and eigenvalue theory of tensors

Journal of Symbolic Computation
Criterions for the positive definiteness of real supersymmetric tensors

Journal of Computational and Applied Mathematics

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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.