线性特征值问题在模态坐标系中的矩阵摄动法

Matrix Perturbation Method in Modal Coordinate System for Linearly Generalized Eigenvalue Problem

本文在文献[1,2]的基础上进一步探讨了对线性广义特征值问题Ax=λBx 进行快速近似重分析的矩阵摄动方法和理论,特别对重特征值情况也完整地导出了特征值和特征向量的直到二阶摄动量的渐近估计算式,并在E.J.Haug 等证明了重特征值的方向可微性的基础上指出对应于重特征值的特征向量在一定意义上也是方向可微的。算例表明本文的算法是正确、有效的。

On the basis of Refs.[1,2],the matrix perturbation method and theory forefficient approximate reanalyses of the linearly generalized eigenvalue problemAχ=λBχ are further studied.Particularly,the asymptotic estimate formulas upto second-order perturbation components for repeated eigenvalues and correspo-nding eigenvectors are also derived completely.Besides,based on the theorem,proved by E.J.Haug et.al.,for directional differentiability of repeated eigen-values,it is further pointed out that the eigenvectors associated with a repeatedeigenvalue are,in a sense,also directionally differentiable.The correctness andeffectiveness of the algorithm presented in this paper are demonstrated byseveral numerical examples.