摘要
本文提供了求解Lyapunov矩阵方程的一个新算法。首先,对系数矩阵具有Frobenius形式的方程给出了一种公式解法。然后通过对系数矩阵的约化,将解法推广列一般情形。最后,给出了数值例子,并同有关的方法进行了比较。
This paper presents a new algorithm for solving the Lyapunov matrix equation. Firstly, it gives a solution formulae to the equation of which the coefficient matrices are Frobenius matrices. Then, this method of solution is extended to common cases through transforming the coefficient matrices. Finally, this paper also gives some calculation examples, and makes the comparison of this method to some other relative methods.
关键词
LYAPUNOV
矩阵方程
矩阵
数值解
matrics, numerical solution,similarity transformation, companion matrix, matrix equation
