| 主子阵约束下矩阵方程AX=B的对称最小二乘解 |
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| 引用本文： | 龚丽莎,胡锡炎,张磊. 主子阵约束下矩阵方程AX=B的对称最小二乘解[J]. 数值计算与计算机应用, 2006, 27(2): 154-160 |
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| 作者姓名： | 龚丽莎 胡锡炎 张磊 |
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| 作者单位： | 湖南大学应用数学系,长沙,410082 |
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| 基金项目： | 国家自然科学基金资助项目(10571047) |
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| 摘 要： | 本文主要讨论主子阵约束下矩阵方程AX=B的对称最小二乘解．基于投影定理,巧妙的把最小二乘问题转化为等式问题求解,并利用奇异值分解的方法,给出了该对称最小二乘解的一般表达式．此外,文章还考虑了此对称最小二乘解集合对任一给定矩阵的最佳逼近问题,得到了最佳逼近解,并给出了相应的算法步骤和数值例子．
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| 关 键 词： | 矩阵方程 Frobenius范数 最小二乘解 最佳逼近 |
| 修稿时间： | 2005-06-30 |
THE SYMMETRIC LEAST-SQUARES SOLUTIONS OF MATRIX EQUATION AX = B WITH A SUBMATRIX CONSTRAINT |
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| Gong Lisha,Hu Xiyan,Zhang Lei. THE SYMMETRIC LEAST-SQUARES SOLUTIONS OF MATRIX EQUATION AX = B WITH A SUBMATRIX CONSTRAINT[J]. Journal on Numerical Methods and Computer Applications, 2006, 27(2): 154-160 |
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| Authors: | Gong Lisha Hu Xiyan Zhang Lei |
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| Abstract: | This paper mainly discusses the symmetric least-squares solutions of matrix equation AX = B with a submatrix constraint. Based on the projection theorem, the least-squares problem is transformed into an equation problem. And by using the method of singular value decomposition(SVD), the general expression of the symmetric least-squares solutions is obtained. Furthermore, to an given matrix, the optimal approximation problem in the solution set is considered.As for this problem, the optimal approximation solution, a numerical algorithm and a numerical example are provided. |
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| Keywords: | matrix equation Frobenius norm least-squares solution optimal approximation |
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