四阶弱对称非负张量Z-谱半径的上下界及应用

针对四阶张量Z-谱半径的估计问题,利用张量Z-特征值的定义,并结合不等式放缩技巧,给出了四阶弱对称非负张量Z-谱半径的新上下界,改进了现有一些结果.作为应用,由Z-谱半径的上界给出了张量最佳秩一逼近和贪婪秩一更新算法收敛速度的下界,由Z-谱半径的上下界给出了具有非负振幅对称纯态纠缠的几何度量的上下界.

Upper and lower bounds for the Z-spectral radius of fourth-order weakly symmetric nonnegative tensors and their applications

For the bounds of fourth-order tensors, by using the definition of Z-eigenvalues of tensors and some techniques of inequalities, new upper and lower bounds for the Z-spectral radius of fourth-order weakly symmetric nonnegative tensors are obtained and proved to be an improvement of some existing result. As applications, new lower bounds for the best rank-one, approximation of tensors and the convergence rate of the greedy rank-one, update algorithm are given, and lower and upper bounds for symmetric pure state with nonnegative amplitudes are obtained by using upper and lower bounds of the Z-spectral radius of tensors.