| 矩阵方程AX=B的Hermitian-广义Hamiltonian矩阵解的迭代算法 |
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| 引用本文： | 杨斌,周富照.矩阵方程AX=B的Hermitian-广义Hamiltonian矩阵解的迭代算法[J].湖南文理学院学报(自然科学版),2011,23(1):14-18. |
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| 作者姓名： | 杨斌 周富照 |
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| 作者单位： | 长沙理工大学数学与计算科学学院,湖南长沙,410114 |
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| 摘 要： | 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.
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| 关 键 词： | 正交投影 最佳逼近解 极小范数解 Hermitian-广义Hamiltonian矩阵 |
The iteration method for the matrix equation AX=B over Hermitian generalized Hamiltonian matrices |
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| YANG Bin,ZHOU Fu-zhao.The iteration method for the matrix equation AX=B over Hermitian generalized Hamiltonian matrices[J].Journal of Hunan University of Arts and Science:Natural Science Edition,2011,23(1):14-18. |
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| Authors: | YANG Bin ZHOU Fu-zhao |
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| Institution: | YANG Bin,ZHOU Fu-zhao (College of Mathematics & Computer Science,Changsha University of Science & Technology,Changsha 410014,China) |
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| Abstract: | 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. |
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| Keywords: | orthogonal projection optimal approximation least-norm solution Hermitian generalized Hamiltonian matrices |
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