| 多参数二次特征值问题重特征值的灵敏度分析 |
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| 引用本文： | 解惠青,戴华.多参数二次特征值问题重特征值的灵敏度分析[J].计算数学,2006,28(1):75-88. |
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| 作者姓名： | 解惠青 戴华 |
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| 作者单位： | 1. 华东理工大学数学系,上海,200237
2. 南京航空航天大学数学系,南京,210016 |
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| 摘 要： | 本文研究解析依赖于多参数的二次特征值问题重特征值的灵敏度分析,得到了重特征值的方向导数,证明了相应的特征向量矩阵和特征值平均值的解析性,给出了其一阶偏导数的表达式．然后以这些结论为基础,定义了二次特征值问题重特征值及其不变子空间的灵敏度,并给出了确定二次特征值问题所含矩阵中敏感元素的方法．
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| 关 键 词： | 灵敏度分析 二次特征值问题 重特征值 方向导数 偏导数 多参数 |
| 收稿时间： | 2005-05-27 |
| 修稿时间： | 2005-05-27 |
ON THE SENSITIVITY OF MULTIPLE EIGENVALUES OF QUADRATIC EIGENVALUE PROBLEMS DEPENDENT ON SEVERAL PARAMETERS |
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| Xie Huiqing,Dai Hua.ON THE SENSITIVITY OF MULTIPLE EIGENVALUES OF QUADRATIC EIGENVALUE PROBLEMS DEPENDENT ON SEVERAL PARAMETERS[J].Mathematica Numerica Sinica,2006,28(1):75-88. |
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| Authors: | Xie Huiqing Dai Hua |
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| Institution: | Department of Mathematics, ECUST, Shanghai 200237, China;Department of Mathematics, NUAA, Nanjing 210016, China |
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| Abstract: | This paper investigates the sensitivity of multiple eigenvalues and corresponding eigenvector matrices of a quadratic eigenvalue problem analytically dependent on several parameters. The directional derivatives of the multiple eigenvalues are obtained. The corresponding eigenvector matrices and the average of eigenvalues are proved to be analytical, and their partial derivatives are given. Using these results, the sensitivity of the multiple eigenvalues and corresponding invariant sub-spaces are defined, and the sensitive elements of matrices involved in quadratic eigenvalue problems can be determined. |
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| Keywords: | sensitivity analysis quadratic eigenvalue problem multiple eigenvalue directional derivatives partial derivatives several parameters |
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