收稿日期: 2016-12-05
网络出版日期: 2017-02-28
基金资助
国家自然科学基金资助项目(11371243); 上海市教委创新基金资助项目(13ZZ068); 上海市重点学科建设资助项目(S30104)
A preconditioning iterative algorithm for eigenvalue problem of symmetric tensor
Received date: 2016-12-05
Online published: 2017-02-28
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.
关键词： Newton法; Newton预处理方法; 移位对称高阶幂法
顾传青, 李龙 . 对称张量特征值问题的一种预处理迭代算法[J]. 上海大学学报(自然科学版), 2017 , 23(1) : 68 -72 . DOI: 10.3969/j.issn.1007-2861.2016.07.009
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.
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