A convergent Newton algorithm for computing Z-eigenvalues of an almost nonnegative irreducible tensor

ABSTRACT

In this paper, we compute Z-eigenvalues of a class of tensors by studying the properties of semi-symmetric tensor. We prove that $\mathcal{A}{x}^{m-1}$ is identical to zero if and only if ${\mathcal{A}}_s=0$, where ${\mathcal{A}}_s$ is the associated semi-symmetric tensor of $\mathcal{A}$. 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.

KEYWORDS:

• Z-eigenvalue
• Newton method
• almost nonnegative irreducible tensor

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Qin Ni  http://orcid.org/0000-0002-1039-8927

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China under grants 11771210, 11571169, and the Natural Science Foundation of Jiangsu Higher Education Institutions of China (17KJD110003), and Qing Lan Project.