矩阵方程组A_1XB_1=C_1,A_2XB_2=C_2的迭代算法

An Iterative Method for the System of Matrix Equations A_1XB_1=C_1,A_2XB_2=C_2

矩阵方程组的求解在结构设计、参数识别、生物学、电学、分子光谱学、固体力学、自动控制理论、振动理论、有限元、线性最优控制等领域都有着重要应用。本文从解线性代数方程组的共轭梯度法中受到启示,不是采用传统的矩阵分解的方法,而是采用迭代算法给出了求矩阵方程组A1XB1=C1,A2XB2=C2的解、极小范数解及其最佳逼近解的方法。

The problem of the system of matrix equations have been widely used in structural design, parametre identification, biology, electricity,molecular spectroscopy, solid mechanics, automatic comrol theory, vibration theory, finite elements, linear optimal control and so on. Many references have obtained a series important result by means of matrices decompositions, In this paper,we use an itemtive method successfully in finding the solution of Matrix Equations A1 XB1 =C1 ,A2XB2 =C2 and its least-norm solution optimal approximation solution with the help of the method of convergence of conjugate.