张量扩展特征值的带位移幂法和共轭梯度法  

Shifted Power Method and Conjugate Gradient Method for Extension Eigenvalues of Tensor

作　　者：王佳佳[1] 赵金玲[1] 徐尔[1] 

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《河南科技大学学报（自然科学版）》2016年第1期83-87,9,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11101028);北京高校青年英才计划基金项目(YETP0385)

摘　　要：针对与牛顿迭代相关的张量扩展特征值问题,在幂法的基础上,提出了求解特征值与特征向量的带位移幂法和共轭梯度法。分析了这两种算法的收敛性,并通过数值试验初步验证了其有效性,同时对两种算法进行了比较。Tensor eigenvalue problem associated with the Newton iteration method was studied in this paper.Based on the existing power method,the shifted power method and conjugate gradient method were proposed to calculate the extension eigenvalue and the corresponding eigenvector of tensor. Then the convergence of these two algorithms was proved. Finally,numerical results showed that the methods were effective. These two methods via numerical experiments were compared.

关 键 词：牛顿法 张量 特征值 带位移幂法 共轭梯度法 收敛性 

分 类 号：O241.6[理学—计算数学]