| 矩阵方程AXB+CYD=E对称最小范数最小二乘解的极小残差法 |
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| 引用本文： | 方玲,廖安平,雷渊.矩阵方程AXB+CYD=E对称最小范数最小二乘解的极小残差法[J].高等学校计算数学学报,2010,32(1). |
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| 作者姓名： | 方玲 廖安平 雷渊 |
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| 作者单位： | 1. 后勤工程学院基础部,重庆,401311
2. 湖南大学数学与计量经济学院,长沙,410082 |
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| 摘 要： | <正>1引言本文用R~(n×m)表示全体n×m实矩阵集合,用SR~(n×n)表示全体n×n实对称矩阵集合,OR~(n×n)表示全体n×n实正交矩阵集合.用I_n表示n阶单位矩阵,用A*B表示矩阵A与B的Hadamard乘积.对任意矩阵A,B∈R~(n×m),定义内积〈A,B〉=tr(B~T A),其中
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| 关 键 词： | 残差法 矩阵方程 最小二乘解 最小范数解 |
A MINIMAL RESIDUAL ALGORITHM FOR THE INCONSISTENT MATRIX EQUATION AXB + CYD = E OVER SYMMETRIC MATRICES |
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| Fang Ling,Liao Anping Lei Yuan.A MINIMAL RESIDUAL ALGORITHM FOR THE INCONSISTENT MATRIX EQUATION AXB + CYD = E OVER SYMMETRIC MATRICES[J].Numerical Mathematics A Journal of Chinese Universities,2010,32(1). |
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| Authors: | Fang Ling Liao Anping Lei Yuan |
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| Institution: | Fang Ling (Dept.of Foundation Studies,Logistical Engineering University of PLA,Chongqing 401311) Liao Anping Lei Yuan (College of Mathematics and Econometrics,Hunan University,Changsha 410082) |
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| Abstract: | An iterative method based on the idea of the classical CG method for the matrix equation AXB + CYD = E is constructed in this paper.By this method,the least-norm least-squares solutions for symmetric matrices can be obtained within finite iteration steps by choosing a special kind of initial iteration matrix when the matrix is not consistent and an error bound is given.Finally, some numerical examples show that the method proposed is quite efficient. |
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| Keywords: | symmetric matrix least-squares solution least norm solution iteration method |
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