| 循环矩阵反问题的最小二乘解 |
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| 引用本文： | 张湘林,李云翔.循环矩阵反问题的最小二乘解[J].湖南师范大学自然科学学报,2011,34(5):17-21. |
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| 作者姓名： | 张湘林 李云翔 |
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| 作者单位： | 湖南城市学院数学与计算科学学院,中国益阳,413000 |
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| 基金项目： | 湖南省教育厅基金资助项目(10C0501); 湖南城市学院教改基金资助项目(2011) |
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| 摘 要： | 讨论了一类循环矩阵反问题的最小二乘解,给出了解的存在定理和解的一般表达式.考虑了给定矩阵的最佳逼近问题,证明了问题存在唯一解,给出了唯一解的表达式,最后给出了两个数值算例.
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| 关 键 词： | 循环矩阵 矩阵反问题 矩阵范数 最小二乘解 |
Least-Square Solution to Inverse Problem of Circulant Matrices |
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| ZHANG Xiang-lin,LI Yun-xiang.Least-Square Solution to Inverse Problem of Circulant Matrices[J].Journal of Natural Science of Hunan Normal University,2011,34(5):17-21. |
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| Authors: | ZHANG Xiang-lin LI Yun-xiang |
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| Institution: | ZHANG Xiang-lin*,LI Yun-xiang(College of Mathematics and Computing Science,Hunan City University,Yiyang 413000,China) |
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| Abstract: | The least-square solution to inverse problem of one kind of circulant matrix is presented.The existence theorems are obtained,and a general representation of such a matrix is presented.In addition,the nearst matrix problem for the given matrix is discussed.The unique nearst matrix solution and an expression for this nearest matrix is provided.Two examples are given at last. |
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| Keywords: | circulant matrix matrix inverse problem matrix norm the least-square solution |
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