| 一类矩阵方程组的正交投影迭代解法 |
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| 引用本文： | 周富照,田时宇,袁艳杰.一类矩阵方程组的正交投影迭代解法[J].吉首大学学报(自然科学版),2015,36(3):1-6. |
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| 作者姓名： | 周富照 田时宇 袁艳杰 |
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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 410004) |
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| 基金项目： | 国家自然科学基金资助项目(11371072) |
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| 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.
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| 关 键 词： | 矩阵方程组 一般解 正交投影迭代法 最佳逼近解 极小范数解 |
An Orthogonal Projection Iteration Method for a Matrix Equations |
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| ZHOU Fuzhao
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TIAN Shiyu
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YUAN Yanjie.An Orthogonal Projection Iteration Method for a Matrix Equations[J].Journal of Jishou University(Natural Science Edition),2015,36(3):1-6. |
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| Authors: | ZHOU Fuzhao TIAN Shiyu YUAN Yanjie |
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| Institution: | (College of Mathematics and Computing Science,Changsha University of Science and Technology,Changsha 410004,China) |
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| Abstract: | An orthogonal projection iteration method for matrix equations AX=B,XC=D is 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. |
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| Keywords: | matrix equations general solution orthogonal projection iteration method optimal approxima-tion minimum norm solution |
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