矩阵方程AXA^T=B行反对称解的正交投影迭代法  

Orthogonal projection iterative method for matrix equation AXA^T=B over row anti-symmetric matrices

作　　者：冯敏[1] 周富照[1] 刘将[1] 

机构地区：[1]长沙理工大学数学与计算科学学院,湖南长沙410076

出　　处：《湖南文理学院学报（自然科学版）》2012年第1期19-23,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省教育厅资助项目(10C0370)

摘　　要：讨论了矩阵方程AXAT=B的行反对称解及其最佳逼近的正交投影迭代解法,首先利用行反对称矩阵类的结构与性质、正交投影及奇异值分解,构造迭代算法,证明了算法的收敛性,得出了收敛速率的估计式;其次给出数值实例,验证了算法的有效性.The orthogonal projection iteration methods are discussed for the matrix equation over row anti-symmetric matrices.Firstly,by using the structure and characteristic properties of the row anti-symmetric matrices and orthogonal projection and SVD,the iteration method is constructed.The convergence of the method is proven.,the estimation of the convergence rate is derived.In addition,some numerical examples are given to verify the effectiveness of the iteration method.

关 键 词：约束矩阵方程 正交投影迭代法 最佳逼近解 极小范数解 

分 类 号：O241.6[理学—计算数学]