首先,将求解不同阶对称张量组的Z-特征值问题转化为非线性函数的极小值问题.当Newton方向与非线性函数负梯度方向夹角的余弦值小于取定的某一固定值时,对下降方向进行改进,从而提出改进的Newton-法求解不同阶对称张量组的Z-特征值.其次...首先,将求解不同阶对称张量组的Z-特征值问题转化为非线性函数的极小值问题.当Newton方向与非线性函数负梯度方向夹角的余弦值小于取定的某一固定值时,对下降方向进行改进,从而提出改进的Newton-法求解不同阶对称张量组的Z-特征值.其次,理论证明改进Newton-法是全局超线性收敛的.最后,数值实例表明,与带位移对称高阶幂法(shifted symmetric high order power method,SS-HOPM)相比,改进Newton-法能够计算出更多的Z-特征值和特征向量,且所用的时间更短.展开更多
In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singul...In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singular vector tuple of a generic tensor is nondegenerate, and(ⅱ) each nonzero Zeigenvector/singular vector tuple of an orthogonally decomposable tensor is nondegenerate.展开更多
文摘首先,将求解不同阶对称张量组的Z-特征值问题转化为非线性函数的极小值问题.当Newton方向与非线性函数负梯度方向夹角的余弦值小于取定的某一固定值时,对下降方向进行改进,从而提出改进的Newton-法求解不同阶对称张量组的Z-特征值.其次,理论证明改进Newton-法是全局超线性收敛的.最后,数值实例表明,与带位移对称高阶幂法(shifted symmetric high order power method,SS-HOPM)相比,改进Newton-法能够计算出更多的Z-特征值和特征向量,且所用的时间更短.
基金supported by National Natural Science Foundation of China(Grant No.11771328)Young Elite Scientists Sponsorship Program by Tianjin and the Natural Science Foundation of Zhejiang Province of China(Grant No.LD19A010002)。
文摘In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singular vector tuple of a generic tensor is nondegenerate, and(ⅱ) each nonzero Zeigenvector/singular vector tuple of an orthogonally decomposable tensor is nondegenerate.
