非对称广义特征值问题重特征值的灵敏度分析

研究非对称广义特征值问题半单重特征值的灵敏度分析。对于解析依赖于多参数的非对称广义特征值问题．给出了半单重特征值的方向导数，证明了相应的广义不变子空间的解析性，并给出了其一阶导数的表达式。以这些结论为基础，定义了半单重特征值及相应的广义不变子空间的灵敏度，并给出了一个确定矩阵束中敏感元素的方法。本文的结论可应用于模型修正、故障诊断与系统最优控制。

Sensitivity Analysis of Multiple Eigenvalues of Non-Symmetric Generalized Eigenvalue Problems

The sensitivity analysis for semisimple multiple eigenva lues of non-symmetric generalized eigenvalue problems is considered. The direct ional derivatives of the multiple eigenvalues of non-symmetric generalized eige nvalue problems analytically dependent on several parameters are obtained, and t he corresponding generalized invariant subspaces are proved to be analytical. Ba sed on these conclusions, the sensitivity of the semisimple multiple eigenvalues and its corresponding generalized invariant subspaces is defined and the determ ination of sensitive elements is discussed. It is useful for structural optimal design, model updating, and structural damage detection.