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.

中文翻译：

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用于计算几乎非负不可约张量的Z特征值的收敛牛顿算法

本文通过研究半对称张量的性质来计算一类张量的Z-特征值。我们证明$\mathcal{一种}{X}^{米-\mathrm{1个}}$ 当且仅当等于 ${\mathcal{一种}}_s=0$，在哪里 ${\mathcal{一种}}_s$ 是的相关半对称张量 $\mathcal{一种}$。基于半对称性质，定义了一个几乎非负的不可约张量。并且我们使用牛顿法来计算这种张量的Z-特征值。可以保证所提算法的收敛性。数值结果被报道以说明我们算法的效率。