A convergent Newton algorithm for computing Z-eigenvalues of an almost nonnegative irreducible tensor. (3rd March 2020)

• Record Type: Journal Article
• Authors: Zhang, Xin; Ni, Qin; Ge, Zhili
• Is Part Of: Optimization methods and software. Volume 35:Number 2(2020)
• Page Start: 377
• Page End: 393
• Publication Date: 2020-03-03
• Subjects: Z-eigenvalue -- Newton method -- almost nonnegative irreducible tensor; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1647196
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: In this paper, we compute Z-eigenvalues of a class of tensors by studying the properties of semi-symmetric tensor. We prove that A x m − 1 is identical to zero if and only if A s = 0, where A s is the associated semi-symmetric tensor of A . Based on the semi-symmetric property, an almost nonnegative irreducible tensor is defined. And we use Newton method to compute Z-eigenvalues of this kind of tensor. The convergence of the proposed algorithm can be guaranteed. Numerical results are reported to illustrate the efficiency of our algorithm.