Improved modal truncation method for eigensensitivity analysis of asymmetric matrix with repeated eigenvalues  

作　　者：张振宇 

机构地区：[1]Department of Applied Mathematics, Shanghai University of Finance and Economics

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第4期437-452,共16页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11101149);the Basic Academic Discipline Program of Shanghai University of Finance and Economics(No.2013950575)

摘　　要：An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜ 〈｜〈s＋1｜ （s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜ 〈｜〈s＋1｜ （s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.

关 键 词：modal truncation method eigenvector derivative asymmetric matrix repeated eigenvalue 

分 类 号：O241.6[理学—计算数学]