The dominant eigenvalue of an essentially nonnegative tensor. Issue 6 (8th April 2013)

• Record Type: Journal Article
• Authors: Zhang, L. P.; Qi, L. Q.; Luo, Z. Y.; Xu, Y.; Lim, Lek‐Heng; Ng, Michael K.; Qi, Liqun
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 6(2013:Nov.)
• Page Start: 929
• Page End: 941
• Publication Date: 2013-04-08
• Subjects: Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.1880
• Languages: English
• ISSNs: 1070-5325

Abstract

<abstract abstract-type="main" id="nla1880-abs-0001"> <title>SUMMARY</title> <p id="nla1880-para-0001">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 &amp; Sons, Ltd.</p> </abstract>