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

In this paper, we compute Z-eigenvalues of a class of tensors by studying the properties of semi-symmetric tensor. We prove that Axm−1 is identical to zero if and only if As=0, where As 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.