| 一类矩阵反问题的扰动分析 |
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| 引用本文： | 戴华. 一类矩阵反问题的扰动分析[J]. 南京航空航天大学学报(英文版), 2000, 17(2) |
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| 作者姓名： | 戴华 |
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| 作者单位： | 南京航空航天大学理学院南京,210016 |
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| 基金项目： | 中国科学院资助项目,国家自然科学基金,江苏省青蓝工程项目,江苏省333新世纪科学技术带头人培养工程 |
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| 摘 要： | 考虑一类矩阵反问题minA∈1A‖A-(A)‖F,其中lA={A∈(X)n×m|‖AX-B‖F＝min},(A)∈(X)n×m,x∈m×p,B∈(X) n×p是给定的矩阵,讨论了当A,X,B有扰动时问题解的稳定性,作出了问题解的扰动分析,对相容和不相容两种情况给出了解的扰动上界.所获得的扰动上界是相对于扰动解到无扰动流形的距离.
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| 关 键 词： | 矩阵 反问题 最佳逼近 扰动分析 |
PERTURBATION ANALYSIS OF A CLASS OF MATRIX INVERSE PROBLEMS |
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| Dai Hua. PERTURBATION ANALYSIS OF A CLASS OF MATRIX INVERSE PROBLEMS[J]. Transactions of Nanjing University of Aeronautics & Astronautics, 2000, 17(2) |
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| Authors: | Dai Hua |
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| Abstract: | A class of matrix inverse problems minimizing‖A-(r)‖F on the linear manifold lA={A∈(X)n×m|‖AX-B‖F =min}is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold. |
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| Keywords: | matrix inverse problem best approximation perturbation analysis |
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