g-循环矩阵反问题的最小二乘解

Least-Square Solutions of Inverse Problem for g-Circulant Matrices

讨论了g-循环矩阵反问题的最小二乘解,得到了通解的表达式,给出了该问题有解的充要条件,并讨论了其最佳逼近问题,证明了逼近矩阵的存在惟一性且给出具体表达式。

In this paper, the least - square solutions of the inverse problem of g - circulant matrices are discussed, and the expression of the general solution is obtained. In addition,the necessary and sufficient conditions about the problem are derived,the problem of the optimal approximation to a given matrix is discussed.At last,the existence and uniqueness of approximation matrices is proved,and the concrete expression of it is provided.