Modal sensitivities for repeated eigenvalues and eigenvalue derivatives

AIAA Journal ◽  
1992 ◽  
Vol 30 (3) ◽  
pp. 850-852 ◽  
Author(s):  
Jinsiang Shaw ◽  
Suhada Jayasuriya
Keyword(s):  
Repeated Eigenvalues ◽  
Eigenvalue 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.

Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues

1993 ◽  
Author(s):  
Yong-Qiang Zhang ◽  
Wen-Liang 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 Dailey 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 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 multi-groups of repeated first eigenvalue derivatives occur. Numerical Examples are given to demonstrate the effectiveness of the proposed method.

Inverse sensitivity method to self-adjoint systems with repeated eigenvalues

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 933-938
Author(s):  
H. W. Song ◽  
L. F. Chen ◽  
W. L. Wang
Keyword(s):  
Adjoint Systems ◽  
Repeated Eigenvalues ◽  
Sensitivity Method

Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

2021 ◽  
pp. 1-16
Author(s):  
Alexander Dabrowski
Keyword(s):  
General Type ◽  
Differential Operators ◽  
Laplacian Operator ◽  
Variational Characterization ◽  
Repeated Eigenvalues ◽  
Direct Extension ◽  
Asymptotic Formulae ◽  
Elliptic Differential Operators ◽  
Domain Perturbations ◽  
Boundary Deformation

A variational characterization for the shift of eigenvalues caused by a general type of perturbation is derived for second order self-adjoint elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some examples of particular interest are presented theoretically and numerically for the Laplacian operator for the following domain perturbations: excision of a small hole, local change of conductivity, small boundary deformation.

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
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