矩阵方程A^TXB+B^TX^TA=C的一般解及其最佳逼近解  

General Solution of Matrix Equation A^TXB +B^TX^TA =C and Its Optimal Approximation Solution

作　　者：雷茂俊 孙波[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,长沙410000

出　　处：《数学理论与应用》2015年第4期47-51,共5页Mathematical Theory and Applications

摘　　要：用正交投影迭代法讨论了矩阵方程A^TXB+B^TX^TA=C的一般解及相应的最佳逼近解.首先利用矩阵的相关理论,给出了求矩阵方程的正交投影迭代解法,证明了算法的收敛性,并得出了收敛速率估计式;其次对该算法稍加修改,得到相应的最佳逼近.本文中,要求A,B实正规矩阵,且满足A^TB=BA^T,C是实矩阵.In this paper the general solution and the optimal approximation solution to the matrix equation ATXB ＋ BTXTA= C, where both A and B are real normal matrices satisfyingATB = BAT , are investigated. Firstly, an orthogonal projection iteration algorithm is designed for solving the matrix equation. The conver- gence of the algorithm is proved and the convergence rate is estimated. Secondly, the algorithm is modified slightly to obtain an optimal approximation solution.

关 键 词：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]