| 矩阵方程AXAT=B行反对称解的正交投影迭代法 |
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| 引用本文： | 冯敏,周富照,刘将. 矩阵方程AXAT=B行反对称解的正交投影迭代法[J]. 湖南文理学院学报(自然科学版), 2012, 24(1): 19-23. DOI: 10.3969/j.issn.1672-6164.2012.01.006 |
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| 作者姓名： | 冯敏 周富照 刘将 |
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| 作者单位： | 1.长沙理工大学数学与计算科学学院,湖南长沙,410076;2.长沙理工大学数学与计算科学学院,湖南长沙,410076;3.长沙理工大学数学与计算科学学院,湖南长沙,410076 |
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| 基金项目： | 湖南省教育厅资助项目(10C0370) |
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| 摘 要： | 讨论了矩阵方程AXAT=B的行反对称解及其最佳逼近的正交投影迭代解法,首先利用行反对称矩阵类的结构与性质、正交投影及奇异值分解,构造迭代算法,证明了算法的收敛性,得出了收敛速率的估计式;其次给出数值实例,验证了算法的有效性.
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| 关 键 词： | 约束矩阵方程 正交投影迭代法 最佳逼近解 极小范数解 |
Orthogonal projection iterative method for matrix equation AXA~T=B over row anti-symmetric matrices |
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| FENG Min,ZHOU Fu-zhao,LIU Jiang. Orthogonal projection iterative method for matrix equation AXA~T=B over row anti-symmetric matrices[J]. Journal of Hunan University of Arts and Science:Natural Science Edition, 2012, 24(1): 19-23. DOI: 10.3969/j.issn.1672-6164.2012.01.006 |
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| Authors: | FENG Min ZHOU Fu-zhao LIU Jiang |
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| Affiliation: | (College of Mathematics and Computing Science,Changsha University of Science and Technology,Changsha 410076,China) |
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| Abstract: | The orthogonal projection iteration methods are discussed for the matrix equation over row anti-symmetric matrices.Firstly,by using the structure and characteristic properties of the row anti-symmetric matrices and orthogonal projection and SVD,the iteration method is constructed.The convergence of the method is proven.,the estimation of the convergence rate is derived.In addition,some numerical examples are given to verify the effectiveness of the iteration method. |
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| Keywords: | constraint matrix equation orthogonal projection iterative method optimal approximate solution least-norm solution |
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