利用对称正交逼近求解对称张量的MSOA算法  

The MSOA Algorithm for Solving Symmetric Tensors by Symmetric Orthogonal Approximation

作　　者：马昌凤 谢亚君 MA CHANGFENG;XIE YAJUN(School of Big Data,Fuzhou University of International Studies and Trade,Fuzhou 350202,China;Key Laboratory of Data Science and Intelligent Computing,Fuzhou University of International Studies and Trade,Fuzhou 350202,China)

机构地区：[1]福州外语外贸学院大数据学院,福州350202 [2]福州外语外贸学院数据科学与智能计算重点实验室,福州350202

出　　处：《应用数学学报》2023年第5期751-768,共18页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11901098);福建省自然科学基金(2022J01378);福建省重大教改(FBJG20200310)资助项目。

摘　　要：本文在Pan等工作的基础上,提出了一种修正的对称正交分解方法(MSOA)来逼近实对称张量.为讨论实对称张量的对称正交逼近,首先将其转化为具有等式约束的极小化问题来进行理论分析,在算法中使用自适应带位移的乘幂法来求解特征向量,同时给出了该算法的收敛性分析.最后通过数值实验验证了对该算法所做的理论分析.数值结果表明,我们提出的算法是稳健和有效的.In this paper,a modified symmetric orthogonal decomposition method(MSOA)is proposed to approximate a real symmetric tensor.In order to discuss the symmetric orthogonal approximation of real symmetric tensors,we firstly translate it into a minimization problem with equality constraints for theoretical analysis.Secondly,in our algorithm,we use an adaptive shifted power method to compute generalized ten-sor eigenvectors and propose the convergence analysis of this algorithm.Finally,the theoretical analysis of the algorithm is verified by numerical experiments.Numerical results show that the proposed algorithm is robust and effective.

关 键 词：对称张量 对称正交分解 收敛性分析 数值实验 

分 类 号：O241[理学—计算数学]