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

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.

AN ITERATIVE ALGORITHM FOR SOLUTIONS OF THE SYSTEM OF MATRIX EQUATIONS A1XB1=C1,A2XB2=C2 OVER LINEAR SUBSPACE

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 A₁XB₁=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.