迭代法求解相容矩阵方程组A_1X+XB_1=C_1,A_2X+XB_2=C_2

Iterative method for constrained matrix equations A_1X+XB_1=C_1,A_2X+XB_2=C_2

对任意初始矩阵,在没有舍入误差的情况下,经过有限步迭代得到问题的一个解。若取特殊初始矩阵,则得到问题的极小范数解。解决了对给定矩阵求最佳逼近解的问题。

For any initial matrix ,a solution can be obtained with finite iteration steps in the absence of round off errors ,w hile a special initial matrix is selected ,the least norm can be obtained .A kind of problem how to get the optimal approximation solution for a given matrix is solved .