一类矩阵方程组的正交投影迭代解法  

An Orthogonal Projection Iteration Method for a Matrix Equations

作　　者：周富照[1] 田时宇[1] 袁艳杰[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410004

出　　处：《吉首大学学报（自然科学版）》2015年第3期1-6,共6页Journal of Jishou University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(11371072)

摘　　要：讨论了矩阵方程组AX=B,XC=D一般解的正交投影迭代解法.利用正交投影原理和一般矩阵的结构、性质构造迭代算法,再利用矩阵的奇异值分解、F-范数的正交不变性及矩阵方程组解的性质,证明了算法的收敛性,且推导出收敛速率的估计式.经数值实例验证了算法的有效性.An orthogonal projection iteration method for matrix equations AX = B ,XC= D is studied . Firstly ,the iterative method is constructed by using the theory of orthogonal projection and the proper‐ties of general matrix ;secondly ,its convergence is proved by using the singular value decomposition ,the orthogonal invariance of F‐norm and the properties for solutions of the matrix equations and the estima‐tion of its convergence rate is obtained;finally ,numerical examples are given to verify the validity of the algorithm .

关 键 词：矩阵方程组 一般解 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]