线性子空间上求解矩阵方程组A_1XB_1=C_1,A_2XB_2=C_2的迭代算法  

AN ITERATIVE ALGORITHM FOR SOLUTIONS OF THE SYSTEM OF MATRIX EQUATIONS A_1XB_1=C_1,A_2XB_2=C_2 OVER LINEAR SUBSPACE

作　　者：周海林[1] 

机构地区：[1]南京理工大学泰州科技学院,泰州225300

出　　处：《计算数学》2017年第2期213-228,共16页Mathematica Numerica Sinica

摘　　要：应用共轭梯度方法,结合线性投影算子,给出迭代算法求解了线性矩阵方程组A_1XB_1=C_1,A_2XB_2=C_2在任意线性子空间上的约束解及其最佳逼近.当矩阵方程组A_1XB_1=C_1,A_2XB_2=C_2相容时,可以证明,所给迭代算法经过有限步迭代可得到矩阵方程组的约束解、极小范数解和最佳逼近.文中的数值例子证实了该算法的有效性.Applying the conjugate gradient method, combined with the linear projection operator, an iterative algorithm is presented to solve the system of linear matrix equations A1XB1 = C1,A2XB2 = C2 for constrained solution and its optimal approximation over any linear subspace. When the system of matrix equations AIXB1 = C1,A2XB2 = C2 is consistent, it is proved that the constrained solution, the least-norm solution and the optimal approximation of the system of matrix equations can be obtained within finite iteration steps by the method. Some numerical examples verify the efficiency of the algorithm.

关 键 词：共轭梯度 投影算子 极小范数解 最佳逼近 

分 类 号：O241.6[理学—计算数学]