判定强H-张量具有线性收敛速度的迭代算法

Iterative Algorithm with Linear Convergence Rate for Determining Strong H-Tensors

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.

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.