Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29937
Title: On the largest eigenvalue of a symmetric nonnegative tensor
Authors: Zhou, G
Qi, L 
Wu, SY
Keywords: Algorithm
Convergence
Convex optimization
Eigenvalue
Symmetric tensor
Issue Date: 2013
Publisher: John Wiley & Sons
Source: Numerical linear algebra with applications, 2013, v. 20, no. 6, p. 913-928 How to cite?
Journal: Numerical linear algebra with applications 
Abstract: In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenvalue-eigenvector; (iii) the minimax theorem is satisfied without requiring the weak irreducibility condition; and (iv) if it is weakly reducible, then it can be decomposed into some weakly irreducible tensors. In addition, the problem of finding the largest eigenvalue of a symmetric nonnegative tensor is shown to be equivalent to finding the global solution of a convex optimization problem. Subsequently, algorithmic aspects for computing the largest eigenvalue of symmetric nonnegative tensors are discussed.
URI: http://hdl.handle.net/10397/29937
ISSN: 1070-5325
EISSN: 1099-1506
DOI: 10.1002/nla.1885
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