| 对称正交对称矩阵反问题的最小二乘解 |
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| 引用本文： | 戴华.对称正交对称矩阵反问题的最小二乘解[J].计算数学,2003,25(1):59-66. |
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| 作者姓名： | 戴华 |
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| 作者单位： | 南京航空航天大学数学系,南京,210016 |
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| 基金项目： | 国家自然科学基金(10271055)，江苏省“青蓝工程”基金资助项目 |
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| 摘 要： | Let P ∈ Rn×n be a symmetric orthogonal matrix. A∈Rn×n is called a symmetric orthogonal symmetric matrix if AT = A and (PA) T = PA. The set of all n × n symmetric orthogonal symmetric matrices is denoted by SRnxnp. This paper discusses the following problems: Problem I. Given X,B∈ Rn×m, find A ∈SRn×np such that||AX - B|| = min Problem II. Given A∈ Rn×n, find A∈SL such thatwhere ||·|| is the Frobenius norm, and SL is the solution set of Problem I.The general form of SL is given. The solvability conditions for the inverseproblem AX = B in SRn×nP are obtained. The expression of the solution toProblem II is presented.
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| 关 键 词： | 对称正交对称矩阵 反问题 最小二乘解 Moore－Penrose广义逆 Hadamard积 Frobenius范数 内积空间 |
| 修稿时间： | 2001年3月23日 |
LEAST-SQUARES SOLUTIONS OF INVERSE PROBLEMS FOR SYMMETRIC ORTHOGONAL SYMMETRIC MATRICES |
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| Dai Hua.LEAST-SQUARES SOLUTIONS OF INVERSE PROBLEMS FOR SYMMETRIC ORTHOGONAL SYMMETRIC MATRICES[J].Mathematica Numerica Sinica,2003,25(1):59-66. |
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| Authors: | Dai Hua |
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| Institution: | Dai Hua(Dept. of Math, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016) |
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| Abstract: | |
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| Keywords: | matrix inverse problem least-squares solution |
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