【摘要】 讨论了矩阵方程组AX=B,XC=D一般解的正交投影迭代解法.利用正交投影原理和一般矩阵的结构、性质构造迭代算法,再利用矩阵的奇异值分解、F-范数的正交不变性及矩阵方程组解的性质,证明了算法的收敛性,且推导出收敛速率的估计式.经数值实例验证了算法的有效性.更多还原

【Abstract】 An orthogonal projection iteration method for matrix equations AX=B,XC=Dis studied.Firstly,the iterative method is constructed by using the theory of orthogonal projection and the properties of general matrix;secondly,its convergence is proved by using the singular value decomposition,the orthogonal invariance of F-norm and the properties for solutions of the matrix equations and the estimation of its convergence rate is obtained;finally,numerical examples are given to verify the validity of the algorithm.更多还原