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.
出处
《应用数学学报》
CSCD
北大核心
2016年第4期610-619,共10页
Acta Mathematicae Applicatae Sinica
关键词
共轭梯度
投影算子
极小范数解
最佳逼近
conjugate gradient
projection operator
least-norm solution
optimal approximation
