一种计算张量的广义特征对的自适应位移梯度法  

An adaptive shifted gradient method for computing generalized eigenpairs of a tensor

作　　者：胡玉婷 季光明[1] 雷黄蕊 洪姗 尹凤 HU Yuting;JI Guangming;LEI Huangrui;HONG Shan;YIN Feng(College of Management Science,Chengdu University of Technology,Chengdu 610059,China;School of Mathematics and Statistics,Sichuan University of Science and Engineering,Zigong 643000,China)

机构地区：[1]成都理工大学管理科学学院,成都610059 [2]四川轻化工大学数学与统计学院,四川自贡643000

出　　处：《成都理工大学学报（自然科学版）》2020年第2期237-244,共8页Journal of Chengdu University of Technology: Science & Technology Edition

基　　金：国家自然科学基金项目(11501392);四川省科技厅应用基础项目(2016JY0249)。

摘　　要：在自适应位移幂法的基础上,提出了一种计算张量广义特征对的自适应位移梯度法,给出了该算法的全局收敛性。自适应位移梯度法通过将当前迭代解与梯度方向的线性组合给出下一个迭代解,从而推广了自适应位移幂法。数值实例结果表明自适应位移梯度法能够应用于计算张量的广义特征对。2种方法的结果对比证明了自适应位移梯度法在一定程度上提高了自适应位移幂法的计算性能。On the basis of the adaptive shifted power method,an adaptive shifted gradient method is proposed to compute generalized eigenpairs of tensor,and the global convergence of the method is obtained.The proposed shifted gradient method constructs the new iterated solution as the linear combination of the current solution and the gradient,thus generalizes the performance of the calculation.Numerical living example shows that the adaptive shifted gradient method can be used to calculate the generalized eigenpairs of tensor.In comparison of the calculation result of adaptive shifted gradient method with that of adaptive shifted power method,the computational performance of adaptive shifted gradient method is improved to some extent over the adaptive shifted power method.

关 键 词：张量 广义特征对 自适应位移幂法 自适应位移梯度法 

分 类 号：O241.6[理学—计算数学]