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
Issue Date: 2013
Source: Numerical linear algebra with applications, 2013, v. 20, no. 6, p. 929-941
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.
Keywords: Algorithm
Convex function
Dominant eigenvalue
Essentially nonnegative tensor
Spectral radius
Publisher: John Wiley & Sons
Journal: Numerical linear algebra with applications 
ISSN: 1070-5325
EISSN: 1099-1506
DOI: 10.1002/nla.1880
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

11
Last Week
0
Last month
0
Citations as of Aug 29, 2020

WEB OF SCIENCETM
Citations

10
Last Week
0
Last month
0
Citations as of Sep 14, 2020

Page view(s)

179
Last Week
3
Last month
Citations as of Sep 15, 2020

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.