非对称系统的特征向量导数的新算法

A new algorithm of computational derivative of eigenvector for asymmetrical system

推导出无阻尼及阻尼非对称系统的特征向量导数的有效算法,其有效性的依据得到证明。首先将特征向量导数表示为一组无关的特征向量的线性组合形式,并通过求解n个线性组合系数来确定特征向量导数。其次通过引入左特征向量,证明特征向量导数所在的支配方程的相容性,并唯一确定n-1个线性组合系数。然后采用与Fox和Kapoor算法类似的策略,把特征向量的归一化条件作为约束方程,从而唯一地确定剩下的那个线性组合系数。该算法公式简洁实用,可操作性强,数值算例证明该算法的正确性及有效性。

In this paper an efficient algorithm whose efficiency is proved erived for the computation of eigenvector derivatives for the undamped and damped asymmetric systems.Firstly,the eigenvector derivative must be a linear combination of the independent eigenvectors.This paper tries to determine n coefficients of linear combination so as to obtain the eigenvector derivative.Secondly,consistency property of dominant equations of derivatives of eigenvectors for asymmetric system is proved by introducing left eigenvectors.Simultaneously,the formula for computing n-1 coefficients of linear combination are generated.By adopting the technique similar to Fox and Kapoor’s algorithm,the rest coefficient is determined.The normalization condition is used as an added equation.Furthermore,their expressions are very simple and exact.Due to the convenience and concision,they are performed easily.Finally,a numerical example is provided to illustrate the accuracy and efficiency of the algorithms.