张量分裂可行域问题的有效投影迭代法  

Efficient Projection Iteration Methods for Solving Tensor Split Feasibility Problem

作　　者：谢亚君 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,福建福州350202 [2]福州外语外贸学院数据科学与智能计算重点实验室,福建福州350202

出　　处：《应用数学》2023年第2期454-463,共10页Mathematica Applicata

基　　金：福建省自然科学基金面上项目(2022J01378);福建省重大教改项目(FBJG20200310);新工科教改项目(J1593419745784GS)。

摘　　要：投影法是解决多集分裂可行域问题的广泛且有效的研究方法.本文从分裂迭代视角出发,研究了求解张量可行域问题的高效投影分裂迭代方法.首先,利用投影算子将张量分裂可行域问题转化为多线性方程组.然后,借助加速超松弛法和对称(交替)加速超松弛法的高维化处理方式,推广到适合多线性方程组的求解框架.最后,通过对新的张量分裂迭代格式的谱半径的理论分析,证明了算法的收敛性.充分的数值测试验证了算法的有效性.Projection method is an extensive and effective method to solve the multi-set split feasibility problem.In this paper,efficient projective splitting iterative methods for solving tensor split feasibility problem are studied from the perspective of splitting iteration.Firstly,the feasibility problem of tensor splitting is transformed into multi-linear equations by projection operator.Furthermore,with the help of the high dimensional processing of the accelerated overrelaxation method and the symmetric(alternating)accelerated overrelaxation method,which is extended to a framework suitable for solving multi-linear equations.Finally,the convergence of the algorithm is proved theoretically by analyzing the spectral radius of the new tensor splitting iterative scheme.The effectiveness of the algorithms are also verified by sufficient numerical tests.

关 键 词：张量分裂可行域问题 多线性方程组 投影分裂法 对称加速超松弛法(SAOR) 谱半径 

分 类 号：O224.2[理学—运筹学与控制论]