| 线性流形上行反对称矩阵反问题的最小二乘解及最佳逼近 |
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| 引用本文： | 梁茂林,代丽芳,杨晓亚.线性流形上行反对称矩阵反问题的最小二乘解及最佳逼近[J].山东大学学报(理学版),2012,47(4):121-126. |
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| 作者姓名： | 梁茂林 代丽芳 杨晓亚 |
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| 作者单位： | 天水师范学院数学与统计学院,甘肃天水,741001 |
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| 基金项目： | 甘肃省教育厅基金资助项目(0808-04;1108B-03);天水师范学院中青年基金资助项目(TSA1104) |
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| 摘 要： | 运用矩阵的奇异值分解方法,给出了线性流形上矩阵方程组AX=B,XC=D的最小二乘行反对称解。对于任意给定矩阵X珟,得到了上述最小二乘解集合中的惟一最佳逼近解。
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| 关 键 词： | 矩阵方程 最小二乘解 行反对称矩阵 奇异值分解 最佳逼近 |
The least-squares solutions and the optimal approximation of the inverse problem for row anti-symmetric matrices on linear manifolds |
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| LIANG Mao-lin,DAI Li-fang,YANG Xiao-ya.The least-squares solutions and the optimal approximation of the inverse problem for row anti-symmetric matrices on linear manifolds[J].Journal of Shandong University,2012,47(4):121-126. |
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| Authors: | LIANG Mao-lin DAI Li-fang YANG Xiao-ya |
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| Institution: | (School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,Gansu,China) |
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| Abstract: | The least-squares row anti-symmetric solutions of matrix equations AX=B,XC=D on linear manifolds are obtained by using the singular value decomposition.Also,for a given matrix,the unique optimal approximation solution in the least-squares solutions set is derived. |
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| Keywords: | matrix equations least-squares solution row anti-symmetric matrix singular value decomposition optimal approximation |
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