关于矩阵方程A^TX+X^TA=B的极小范数解

On the Minimum Norm Solution of the Matrix Equation A^TX+X^TA=B

作者讨论矩阵方程 ATX+ XTA=B。该方程在 Hamilton力学研究中有用。首先利用L yapunov方程证明了极小 Frobenius范数解的存在性和惟一性。然后用奇异值分解给出了求解最小范数解的一种方法。

This paper deals with the matrix equation A TX+X TA=B which resulted from Hamiltonian mechanics. By using Lyapunov theory, the existence of the minimal Frobenius norm solution is proved. Then, a method is presented based on the singular value decomposition to compute the minimal norm solution. Finally, both forward and backward perturbation bounds are obtained.