| 一类线性矩阵方程的最小二乘解 |
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| 引用本文： | 张广强,王文超.一类线性矩阵方程的最小二乘解[J].佳木斯大学学报,2006,24(3):426-427. |
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| 作者姓名： | 张广强 王文超 |
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| 作者单位： | 华北水利水电学院数学与信息科学系 河南郑州450011(张广强)，大连理工大学应用数学系 辽宁大连116024(王文超) |
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| 摘 要： | 利用矩阵的奇异值分解得到Φ=‖ATX XTA-B‖=min的通解,和矩阵方程ATX XTA=B有解的充分必要条件并在有解时给出其一般表达式.
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| 关 键 词： | 最小二乘解 矩阵方程 奇异值分解 |
| 文章编号： | 1008-1402（2006）03-0426-02 |
| 收稿时间： | 2006-03-07 |
| 修稿时间： | 2006年3月7日 |
Least-square Solution of a Kind of Linear Matrix Equation |
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| ZHANG Guang-qiang,WANG Wen-chao.Least-square Solution of a Kind of Linear Matrix Equation[J].Journal of Jiamusi University(Natural Science Edition),2006,24(3):426-427. |
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| Authors: | ZHANG Guang-qiang WANG Wen-chao |
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| Institution: | 1 .Department of Mathematics and Information Sciences, North China Institute of Water Conservancy and Hydroelectric Power, 450011, China; 2 Department of Applied Mathematics, Dalian Univrsity of Technology, Dalian 116024, China |
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| Abstract: | By applying the singular value decomposition(SVD) of matrix,we obtain the general form solutions of,and the sufficient and necessary conditions for the existence of solutions about matrix equation.And we present the explicit expression of general solutions. |
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| Keywords: | least square solution matrix equation singular value decomposition |
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