矩阵方程A×B=C的中心对称解

The Central Symmetric Solution of the Matrix Equation A×B=C

文章研究了矩阵方程的中心对称解。利用矩阵对的广义奇异值分解给出了该方程有中心对称解的充分必要条件,以及解的通式,证明了最佳逼近问题存在唯一解,并给出了求最佳逼近解的算法和数值算例。

The central symmetric solutions of the matrix equation A × B = C are studied. Necessary and sufficient condition for the existence of such solution and their general forms are derived by using generalized singular value decomposition. We prove the existence and the uniqueness of the optimal approximate solution and then give the numerical method and numerical experiments.