酉对称矩阵的满秩分解及其算法

对酉对称矩阵的满秩分解算法作了研究，证明了酉对称矩阵的满秩分解矩阵F^＊和G^＊与母矩阵A的分解矩阵F和G之间的定量关系，同时给出了满秩分解的两种快速算法。最后对酉对称矩阵的部分广义逆-g逆，反射g逆，最小二乘g逆，最小范数g逆问题作了定量分析，也得到了相应的算法，并在文后举例给以说明所得算法大大降低了酉对称矩阵的满秩分解的计算量和存储量，提高了计算效率。

Maximum rank decomposition and algorithm for unitary symmetric matrix

We study the algorithms for the unitary symmetric matrix, and prove the quantitative correspondence of F~*and G~*matrices of unitary symmetric matrices and its mother matrix A.And address two new algorithms for the unitary symmetric matrix at the same time.At last also analyse the Moore-Penrose inverse,e.g.g inverse, reflected ginverse,least square g inverse,least norm g inverse,and give the algorithms of Moore-Penrose inverse for unitary symmetric matrixtoo.Some examples illustrate the applications of the above theory.We can save dramatically the CPU time and memory.