The Perron-Frobenius theorem says that the spectral radius of an irreducible nonnegative tensor is the unique positive eigenvalue corresponding to a positive eigenvector. With this in mind, the purpose of this paper is to find the spectral radius and its corresponding positive eigenvector of an irreducible nonnegative symmetric tensor. By transferring the eigenvalue problem into an equivalent problem of minimizing a concave function on a closed convex set, which is typically a DC (difference of convex functions) programming, we derive a simpler and cheaper iterative method. The proposed method is well-defined. Furthermore, we show that both sequences of the eigenvalue estimates and the eigenvector evaluations generated by the method $Q$-linearly converge to the spectral radius and its corresponding eigenvector, respectively. To accelerate the method, we introduce a line search technique. The improved method retains the same convergence property as the original version. Preliminary numerical results show that the improved method performs quite well.

翻译：摘要：Perron-Frobenius定理指出，不可约非负张量的谱半径是唯一对应于正特征向量的正特征值。基于此，本文旨在寻找不可约非负对称张量的谱半径及其对应的正特征向量。通过将特征值问题转化为在闭凸集上最小化凹函数的等价问题（典型DC规划问题，即凸函数差优化），我们推导出一种更简单且计算成本更低的迭代方法。该方法具有良定义性。进一步证明，该方法生成的估计特征值序列和特征向量序列均以$Q$-线性收敛速度分别收敛于谱半径及其对应的特征向量。为加速该方法，我们引入了一种线搜索技术。改进后的方法保持了与原始版本相同的收敛性质。初步数值实验表明，改进方法具有良好的性能。