In this paper, we propose generalized inverse power methods with variable shifts for finding the smallest H-/Z-eigenvalue and associated H-/Z-eigenvector of symmetric tensors. The methods are guaranteed to always converge to a H-/Z-eigenpair. Furthermore, for an even order nonsingular symmetric $\mathcal{M}$-tensor, the proposed method with any positive initial point always converges to the smallest H-eigenvalue. Numerical results are reported to illustrate that the proposed methods often can find the smallest H-/Z-eigenvalue instead of other H-/Z-eigenvalues of symmetric tensors. Moreover, we can always get the smallest H-eigenvalue for an even order nonsingular symmetric $\mathcal{M}$-tensor.

在本文中，我们提出了具有可变位移的广义逆幂法，用于寻找对称张量的最小 H-/Z-特征值和关联的 H-/Z-特征向量。这些方法保证始终收敛到 H-/Z-特征对。此外，对于偶数阶非奇异对称$\mathcal{米}$-tensor，所提出的具有任何正初始点的方法总是收敛到最小的 H-特征值。数值结果表明，所提出的方法通常可以找到最小的 H-/Z-特征值，而不是对称张量的其他 H-/Z-特征值。此外，我们总是可以得到偶数阶非奇异对称的最小 H-特征值$\mathcal{米}$-张量。