张量具有线性收敛速度的迭代算法

基于计算非负张量谱半径的高阶幂法, 给出一种新的迭代算法判定强H张量. 结合不等式的放缩技巧和非负张量的Perron-Frobenius定理证明所给算法在有限步内停止, 且其收敛速度是线性收敛的. 数值算例表明, 该算法能判定任意给定的张量是否为强H张量, 且在某些情形下比经典的强H张量判定算法所需迭代步数更少.

Iterative Algorithm with Linear Convergence Rate

Based on the higher order power method for computing the spectral radius of nonnegative tensors, we proposed a new iterative algorithm for determining strong H tensors. We proved that the given algorithm stopped in a finite step and its convergence rate was linear convergence by combined with the scaling technique of inequality and Perron Frobenius theorem of nonnegative tensors. Some numerical examples show that the algorithm can determine whether a given tensor is  a strong H tensor or not. The iterative steps of the algorithm are less than that of the classical algorithm for determining strong H tensors in some cases.