线性子空间上求解矩阵方程AXB+CXD=F的迭代算法  

An Iterative Algorithm for Solutions of Matrix Equation AXB+CXD=F 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：《应用数学学报》2016年第4期610-619,共10页Acta Mathematicae Applicatae Sinica

摘　　要：应用共轭梯度法,结合线性投影算子,给出迭代算法求解线性矩阵方程AXB+CXD=F在任意线性子空间上的约束解及其最佳逼近.当矩阵方程AXB+CXD=F有解时,可以证明,所给迭代算法经过有限步迭代可得到矩阵方程的约束解、极小范数解和最佳逼近.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 linear matrix equation AXB＋CXD=r for constrained solution and its optimal approximation over any linear subspace. When the matrix equation AXB＋CXD=F is consistent over solution, it is proved that the constrained solution, the least-norm solution and the optimal approximation of the matrix equation can be obtained within finite iteration steps by this 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：O151.21[理学—数学]