求解广义复Sylvester张量方程的子空间迭代法  

The Subspace Iteration Method for Solving Generalized Complex Sylvester Tensor Equations

作　　者：马昌凤 李清雅[2] MA Changfeng;LI Qingya(School of Big Data&University Engineering Center,Fuzhou University of International Studies and Trade,Fuzhou 350202,China;School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福州外语外贸学院大数据学院高校工程研究中心,福建福州350202 [2]福建师范大学数学与统计学院,福建福州350117

出　　处：《应用数学》2024年第3期601-609,共9页Mathematica Applicata

基　　金：国家自然科学基金(12371378);福建省自然科学基金(2023J011127)。

摘　　要：本文研究求解广义复Sylvester张量方程的修正共轭梯度法(MCG)和共轭梯度最小二乘法(CGLS).它们都基于求解线性方程组的经典Krylov子空间方法.在不计舍入误差的情况下,理论分析表明对于任意初始张量,所提出的算法收敛到Sylvester张量方程的解.数值结果验证了MCG算法和CGLS算法的有效性.In this paper,the modified conjugate gradient(MCG)method and the conjugate gradient least squares(CGLS)method are proposed to solve the generalized complex Sylvester tensor equations.They are all based on the classical Krylov subspace method for solving linear equations.Theoretical analysis shows that the proposed algorithm converges to Sylvester tensor equation solutions for any initial tensors,excluding rounding errors.The numerical results show that the MCG algorithm and CGLS algorithm are effective.

关 键 词：Sylvester张量方程 MCG方法 CGLS方法 收敛性分析 数值实验 

分 类 号：O241[理学—计算数学]