A note on computing eigenvector derivatives with distinct and repeated eigenvalues

Communications in Numerical Methods in Engineering

Volumn 23, Issue 3, 2007, Pages 241-251

  Wu, Baisheng ^a   Xu, Zhonghai ^a   Li, Zhengguang ^a  

^a JILIN UNIVERSITY   (China)

Author keywords

Condition numbers; Distinct and repeated eigenvalues; Eigenvector derivatives; Extended system; Symmetric eigensystem

Indexed keywords

MATHEMATICAL MODELS; NUMERICAL METHODS; VECTORS;

.; COEFFICIENT MATRIX; CONDITION NUMBERS; DISTINCT EIGENVALUES; EIGENVECTOR DERIVATIVES; REPEATED EIGENVALUES;

EIGENVALUES AND EIGENFUNCTIONS;

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; VECTORS;

EID: 33847702141     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.895     Document Type: Article

References (12)

1. Nelson RB. Simplified calculations of eigenvector derivatives. AIAA Journal 1976; 14:1201-1205.
2. Ojalvo IU. Efficient computation of modal sensitivities for systems with repeated frequencies. AIAA Journal 1988; 26:361-366.
3. Mills-Curran WC. Calculation of eigenvector derivatives for structures with repeated eigenvalues. AIAA Journal 1988; 26:867-871.
4. Dailey RL. Eigenvector derivatives with repeated eigenvalues. AIAA Journal 1989; 27:486-491.
5. Mills-Curran WC. Comment on 'Eigenvector derivatives with repeated eigenvalues'. AIAA Journal 1990; 28:1846.
6. Song DT, Han WZ, Chen SH. Simplified calculation of eigenvector derivatives with repeated eigenvalues. AIAA Journal 1996; 34:859-861.
7. Hou GJW, Kenny SP. Eigenvalue and eigenvector approximate analysis for repeated eigenvalue problems. AIAA Journal 1992; 30:2317-2324.
8. Lee IW, Jung GH. An efficient algebraic method for the computation of natural frequencies and mode shape sensitivities - Part I. Distinct natural frequencies. Computers and Structures 1997; 62:429-435.
9. Lee IW, Jung GH. An efficient algebraic method for the computation of natural frequencies and mode shape sensitivities - Part II. Multiple natural frequencies. Computers and Structures 1997; 62:437-443.
10. Andrew AL, Tan RCE. Computation of derivatives of repeated eigenvalues and the corresponding eigenvectors of symmetric matrix pencils. SIAM Journal on Matrix Analysis and Applications 1998; 20:78-100.
11. Gerald CF, Wheatley PO. Applied Numerical Analysis (3rd edn). Addison-Wesley Publishing Company: London, 1984.
12. Golub GH, Van Loan CF. Matrix Computations (3rd edn). Johns Hopkins University Press: Baltimore, London, 1996.