重特征值及其特征向量摄动重分析方法探讨

An Investigation into the Perturbational Reanalysis Method of Repeated Eigenvalues and Associated Eigenvectors

本文基于已有研究结果,进一步探讨了线性广义特征值问题的重特征值及其特征向量摄动重分析理论和方法,阐述了重特征值情形下摄动重分析方法的一些重要特点,完善了重特征值的特征向量的二阶摄动算式,并论证了重特征值摄动法与相异特征值摄动法之间的统一性。还以算例说明了重特征值情形下摄动重分析算法的实施步骤及其有效性。

The perturbational reanalysis method of repeated eigenvalues and associated eigenvectors of the lineargeneralized eigenvalue problem is further investigated on the basis of the relevant results of previous stud-ies.Some important characteristics of the perturbation method are explained,and the unity between theperturbation method for the case of repeated eigenvalues and that for the case of distinct eigenvalues is re-vealed.Two new formulas for perturbational reana]ysis of the eigenvectors associated with repeated eigen-values are set up,which make the reanalysis algorithm up to second-order perturbation terms become per-fect.A numerical example is presented to demonstrate the implementation process and the effectiveness ofthe perturbational reanalysis algorithm for the case of repeated eigenvalues.