Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/27720
Title: The dominant eigenvalue of an essentially nonnegative tensor
Authors: Zhang, LP
Qi, LQ 
Luo, ZY
Xu, Y
Keywords: Algorithm
Convex function
Dominant eigenvalue
Essentially nonnegative tensor
Spectral radius
Issue Date: 2013
Publisher: John Wiley & Sons
Source: Numerical linear algebra with applications, 2013, v. 20, no. 6, p. 929-941 How to cite?
Journal: Numerical linear algebra with applications 
Abstract: It is well known that the dominant eigenvalue of a real essentially nonnegative matrix is a convex function of its diagonal entries. This convexity is of practical importance in population biology, graph theory, demography, analytic hierarchy process, and so on. In this paper, the concept of essentially nonnegativity is extended from matrices to higher-order tensors, and the convexity and log convexity of dominant eigenvalues for such a class of tensors are established. Particularly, for any nonnegative tensor, the spectral radius turns out to be the dominant eigenvalue and hence possesses these convexities. Finally, an algorithm is given to calculate the dominant eigenvalue, and numerical results are reported to show the effectiveness of the proposed algorithm.
URI: http://hdl.handle.net/10397/27720
ISSN: 1070-5325
EISSN: 1099-1506
DOI: 10.1002/nla.1880
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