一类矩阵方程的对称正交对称解的迭代法研究

An Iterative Method for the Symmetric Ortho-symmetric Solutions of a Class of Matrix Equation

研究了求解一类约束矩阵方程及相应的最佳逼近问题的正交投影迭代法.利用对称正交对称矩阵的结构特点及相关性质,并借助一些矩阵空间的相关理论,给出了求矩阵方程AX=B的对称正交对称解的正交投影迭代算法;证明了算法的收敛性,得到了算法的收敛率估计;当方程相容时,该算法收敛于问题的极小范数解,当方程不相容时,该算法收敛于方程的极小范数最小二乘解;对该算法稍加修改后,同样可求出相应的最佳逼近解.

The orthogonal projection iteration for the solutions of a class of constrained matrix equation and the related optimal approximation problem are considered. The iterative method for the symmetric ortho-symmetric solutions to the matrix equation AX=B is given. The convergence of the methods is proved,and the estimations of the convergence rate are given. If the equations are consistent,the method will converge to the least-norm solutions of the equations,and if the equations are not consistent,the method wi...