矩阵广义奇异值分解的一个新证法及推论

A New Proof of Generalized Singular-Value Decomposition

从矩阵对的CS分解理论出发,给出了广义奇异值分解的一个新的证明.给出了关于矩阵对广义奇异值的三个有用的推论.最后给出了计算矩阵对的广义奇异值分解的一个算法.数值实例说明算法是可行且有效的.

The generalized singular-value decomposition of the matrix pair A and B this a powerful tool for solving the constrained matrix equations. With the aid of the CS decomposition of the matrix pair A and B, this paper gave a new proof of the theorem of the generalized singular-value decomposition of the matrix pair A and B. Three useful corollaries on the generalized singular-values of the matrix pair were presented. Finally, an algorithm was also provided to compute the generalized singular-value decomposition of the matrix pairs A and B. Some examples were given to show that the algorithm was both feasible and efficient.