| 矩阵方程组$AX=B,XC=D$的Hermitian自反(反Hermitian自反)最小二乘解及其最佳逼近 |
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| 引用本文： | 周烁,杨士通,王雯.矩阵方程组$AX=B,XC=D$的Hermitian自反(反Hermitian自反)最小二乘解及其最佳逼近[J].数学研究及应用,2011,31(6):1108-1116. |
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| 作者姓名： | 周烁 杨士通 王雯 |
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| 作者单位： | 东北电力大学理学院, 吉林 吉林 132012;东北电力大学理学院, 吉林 吉林 132012;东北电力大学理学院, 吉林 吉林 132012 |
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| 基金项目： | Acknowledgments The authors are very grateful to the referees for valuable comments. |
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| 摘 要： | In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.
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| 关 键 词： | 埃尔米特 自反矩阵 最小二乘解 矩阵方程 矩阵和 最佳逼近问题 一般表达式 分块 |
| 收稿时间： | 2010/6/12 0:00:00 |
| 修稿时间： | 2011/1/12 0:00:00 |
Least-Squares Solutions of Matrix Equations $(AX=B, XC=D)$ for Hermitian Reflexive (Anti-Hermitian Reflexive) Matrices and Its Approximation |
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| Shuo ZHOU,Shi Tong YANG and Wen WANG.Least-Squares Solutions of Matrix Equations $(AX=B, XC=D)$ for Hermitian Reflexive (Anti-Hermitian Reflexive) Matrices and Its Approximation[J].Journal of Mathematical Research with Applications,2011,31(6):1108-1116. |
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| Authors: | Shuo ZHOU Shi Tong YANG and Wen WANG |
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| Institution: | School of Mathematical Sciences, Northeast Dianli University, Jilin 132012, P. R. China |
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| Abstract: | In this paper, the Hermitian reflexive (Anti-Hermitian reflexive) least-squares solutions of matrix equations $(AX=B, XC=D)$ are considered. With special properties of partitioned matrices and Hermitian reflexive (Anti-Hermitian reflexive) matrices, the general expression of the solution is obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is considered. |
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| Keywords: | matrix equations Hermitian reflexive matrix Anti-Hermitian reflexive matrix least-squares solution optimal approximation |
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