矩阵方程AX=B的Hermitian-广义Hamiltonian矩阵解的迭代算法

The iteration method for the matrix equation AX=B over Hermitian generalized Hamiltonian matrices

利用正交投影、Hermitian-广义Hamiltonian矩阵类的结构与性质及奇异值分解,讨论了矩阵方程AX=B的Hermitian-广义Hamiltonian矩阵解及其最佳逼近的迭代算法,证明了算法的收敛性,求出了相应的最佳逼近解,并给出了相应的算法步骤和数值例子.

The iteration method is discussed for the matrix equation AX=B over Hermitian Generalized Hamiltonian Matrices,by the structure and characteristic properties of the Hermitian Generalized Hamiltonian Matrices and the Orthogonal projection Theorem and SVD,the iteration method is constructed and its convergence is proven and the convergence rate is obtained;As for this problem,the optimal approximation solution,a numerical algorithm and a numerical example are provided.