Dynamic flexibility method with hybrid shifting frequency for eigenvector derivatives

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 2047-2052
Author(s):  
D.-W. Zhang ◽  
F.-S. Wei
Keyword(s):  
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

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

Contribution of the truncated modes to eigenvector derivatives

AIAA Journal ◽  
1994 ◽  
Vol 32 (7) ◽  
pp. 1551-1553 ◽  
Author(s):  
Zhong-sheng Liu ◽  
Su-huan Chen ◽  
Min Yu ◽  
You-qun Zhao
Keyword(s):  
Eigenvector Derivatives

scholarly journals Observations on the Computation of Eigenvalue and Eigenvector Jacobians

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 245 ◽  
Author(s):  
Andrew J. Liounis ◽  
John A. Christian ◽  
Shane B. Robinson
Keyword(s):  
Complex Case ◽  
Extensive Literature ◽  
Jacobian Matrices ◽  
Special Cases ◽  
The Matrix ◽  
General Complex ◽  
Analytic Expressions ◽  
And Performance ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector

Many scientific and engineering problems benefit from analytic expressions for eigenvalue and eigenvector derivatives with respect to the elements of the parent matrix. While there exists extensive literature on the calculation of these derivatives, which take the form of Jacobian matrices, there are a variety of deficiencies that have yet to be addressed—including the need for both left and right eigenvectors, limitations on the matrix structure, and issues with complex eigenvalues and eigenvectors. This work addresses these deficiencies by proposing a new analytic solution for the eigenvalue and eigenvector derivatives. The resulting analytic Jacobian matrices are numerically efficient to compute and are valid for the general complex case. It is further shown that this new general result collapses to previously known relations for the special cases of real symmetric matrices and real diagonal matrices. Finally, the new Jacobian expressions are validated using forward finite differencing and performance is compared with another technique.

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
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