广义Sylvester矩阵方程的中心对称类解及其最佳逼近  

The Central Symmetric Class Solution and Optimal Approximation to Generalized Sylvester Matrix Equations

作　　者：周富照 陈露 Zhou Fuzhao;Chen Lu(College of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410004,China)

机构地区：[1]长沙理工大学数学与统计学院,长沙410004

出　　处：《数学理论与应用》2017年第3期1-16,共16页Mathematical Theory and Applications

摘　　要：本文首先利用共轭梯度及矩阵性质,构造迭代算法,并证明算法的收敛性,同时对该算法当方程相容时收敛到问题的极小范数解进行证明.然后,对该算法进行细微修改,应用于相应的最佳逼近问题.最后给出相关的数值实例,验证算法的有效性.In this paper an iterative algorithm for solving the generalized Sylvester matrix equations is firstly constructed by using the conjugate gradients and the matrix properties and the convergence of the algorithm is proved.Furthermore,when the equation is compatible the algorithm is proved to converge to the minimal norm solution to the problem.Then the algorithm is modified slightly to obtain the corresponding optimal approximation.Finally,numerical examples are given to verify the validity of the algorithm.

关 键 词：Sylvester矩阵方程 共轭梯度迭代法 中心对称类解 极小范数解 最佳逼近解 

分 类 号：O241.6[理学—计算数学]