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The dominant eigenvalue of an essentially nonnegative tensor
Author(s) -
Zhang L. P.,
Qi L. Q.,
Luo Z. Y.,
Xu Y.
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1880
Subject(s) - mathematics , convexity , eigenvalues and eigenvectors , spectral radius , tensor (intrinsic definition) , diagonal , regular polygon , combinatorics , pure mathematics , geometry , physics , quantum mechanics , financial economics , economics
SUMMARY 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. Copyright © 2013 John Wiley & Sons, Ltd.