对称张量秩-1近似逆迭代算法  

Inverse Iteration Algorithm for Rank-1 Approximation of Symmetric Tensors

作　　者：朱文凤 盛洲 ZHU Wenfeng;SHENG Zhou(School of Microelectronics and Data Science,Anhui University of Technology,243002,Maanshan,Anhui,China)

机构地区：[1]安徽工业大学微电子与数据科学学院,安徽马鞍山243002

出　　处：《淮北师范大学学报(自然科学版)》2025年第1期16-20,共5页Journal of Huaibei Normal University:Natural Sciences

基　　金：安徽省自然科学基金项目(2208085QA07)。

摘　　要：为得到对称张量秩-1近似分解,提出一个平移逆迭代算法。算法每步迭代子问题转化为计算一个线性方程组,选取适当平移参数保证线性方程组系数矩阵非奇异性,建立逆迭代算法全局收敛性。数值实验表明,算法在运行时间和迭代次数等方面具有较强竞争力。In order to obtain the rank-1 approximate decomposition of symmetric tensors,a shift inverse iteration algorithm is proposed.Each iteration subproblem of the algorithm is transformed into a linear system of equations,and the nonsingularity of the coefficient matrix of the linear equations is guaranteed by selecting appropriate shift parameter,and the global convergence of the inverse iteration algorithm is established.The numerical experiments are reported to illustrate that the algorithm is very competitive in cost time and iteration.

关 键 词：对称张量 秩-1近似 逆迭代 Z-特征对 

分 类 号：O221.2[理学—运筹学与控制论]