摘要
通过推广共轭梯度法思想给出一种迭代算法去求解一般耦合矩阵方程组的广义双对称解,并对算法性质给予介绍说明,将证明若一般耦合矩阵方程组关于广义双对称解相容,那么在不考虑误差的情况下,对于任意给定的初始广义双对称矩阵组,利用所构造出的迭代算法,都能在有限步之内迭代得到其广义双对称解.若取定特殊的初始矩阵,则可获得其极小Frobenius范数约束解,进一步解决最佳逼近问题.
In this paper, by the extension of conjugate gradient method, a iterative algorithm to solve the general coupled matrix equations over the generalized bisymmetric matrices is given. If the general coupled matrix equations are consistent over the generalized bisymmetric matrices, so without considering the machine errors and rounding errors, for any given initial generalized bisymmetric matrices, the generalized bisymmetric solutions can be obtained within limited iterative steps by using the iterative algorithm. Also the least Frobenius norm generalized bisymmetric solutions can be derived by choosing a special king of initial matrices. Furthermore, the optimal approximation problem is solved.
出处
《哈尔滨师范大学自然科学学报》
CAS
2014年第5期23-30,共8页
Natural Science Journal of Harbin Normal University
关键词
一般耦合矩阵方程组
广义双对称解
FROBENIUS范数
最佳逼近解
The general coupled matrix equations
Generalized bisymmetric matrices
Frobenius norm
The optimal approximation solution
