对称张量特征值问题的一种预处理迭代算法

A preconditioning iterative algorithm for eigenvalue problem of symmetric tensor

移位对称高阶幂法(shifted symmetric high order power method,SS-HOPM)是一种求解张量Z-特征值的著名迭代算法.用Newton法对该算法实施初值预条件处理,得到了对称张量特征值问题的一种Newton预条件移位对称高阶幂法(preconditioning SS-HOPM,PSS-HOPM).用两个数值例子验证并得出,与SS-HOPM相比,该算法在几乎不增加计算时间的条件下能计算出更多的特征值.

Shifted symmetric high order power method （SS-HOPM） is a well-known iterative algorithm for solving tensor Z-eigenvalue. In this paper, the Newton method is used to deal with the initial condition of the algorithm. A Newton preconditioning SS-HOPM （PSS-HOPM） for the symmetric tensor eigenvalue problem is obtained. Two numerical examples are used to illustrate that, compared with the SS-HOPM algorithm, this algorithm can calculate more eigenvalues with little increase of computation time.