Comment on "Eigenvector Derivatives with Repeated Eigenvalues"

AIAA Journal ◽  
1990 ◽  
Vol 28 (10) ◽  
pp. 1846-1846 ◽  
Author(s):  
William C. Mills-Curran
Keyword(s):  
Repeated Eigenvalues ◽  
Eigenvector Derivatives

Simplified calculation of eigenvector derivatives with repeated eigenvalues

AIAA Journal ◽  
1996 ◽  
Vol 34 (4) ◽  
pp. 859-862 ◽  
Author(s):  
Da-tong Song ◽  
Wan-zhi Han ◽  
Su-huan Chen ◽  
Zhi-ping Qiu
Keyword(s):  
Repeated Eigenvalues ◽  
Eigenvector Derivatives ◽  
Simplified Calculation

Eigenvector derivatives with repeated eigenvalues

AIAA Journal ◽  
1989 ◽  
Vol 27 (4) ◽  
pp. 486-491 ◽  
Author(s):  
R. Lane Dailey
Keyword(s):  
Repeated Eigenvalues ◽  
Eigenvector Derivatives

Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues

1995 ◽  
Vol 117 (1) ◽  
pp. 207-212 ◽  
Author(s):  
Y.-Q. Zhang ◽  
W.-L. Wang
Keyword(s):  
Recent Work ◽  
New Method ◽  
First Eigenvalue ◽  
Numerical Examples ◽  
Repeated Eigenvalues ◽  
Generalized Eigenproblem ◽  
Eigenvalue Derivatives ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector ◽  
Derivatives Of

A new method is presented for computation of eigenvalue and eigenvector derivatives associated with repeated eigenvalues of the generalized nondefective eigenproblem. This approach is an extension of recent work by Daily and by Juang et al. and is applicable to symmetric or nonsymmetric systems. The extended phases read as follows. The differentiable eigenvectors and their derivatives associated with repeated eigenvalues are determined for a generalized eigenproblem, requiring the knowledge of only those eigenvectors to be differentiated. Moreover, formulations for computing eigenvector derivatives have been presented covering the case where multigroups of repeated first eigenvalue derivatives occur. Numerical examples are given to demonstrate the effectiveness of the proposed method.

The Derivatives of Repeated Eigenvalues and Their Associated Eigenvectors

1996 ◽  
Vol 118 (3) ◽  
pp. 390-397 ◽  
Author(s):  
M. I. Friswell
Keyword(s):  
Taylor Series ◽  
Design Parameters ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
Repeated Eigenvalues ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector ◽  
Derivatives Of

This paper considers the calculation of eigenvalue and eigenvector derivatives when the eigenvalues are repeated. An extension to Nelson’s method is used to calculate the first order derivatives of eigenvectors when the derivatives of the associated eigenvalues are also equal. The continuity of the eigenvalues and eigenvectors is discussed, and the discontinuities in the eigenvectors, when they are regarded as functions of two or more design parameters, is demonstrated. The validity of Taylor series for the eigenvalues and eigenvectors is examined and the use of these series critically assessed.

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