The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Simplified calculation of eigenvector derivatives
Abstract
A simplified procedure is presented for the determination of the derivatives of eigenvectors of nth order algebraic eigensystems. The method is applicable to symmetric or nonsymmetric systems, and requires knowledge of only one eigenvalue and its associated right and left eigenvectors. In the procedure, the matrix of the original eigensystem of rank (/?-!) is modified to convert it to a matrix of rank /?, which then is solved directly for a vector which, together with the eigenvector, gives the eigenvector derivative to within an arbitrary constant. The norm of the eigenvector is used to determine this constant and complete the calculation. The method is simple, since the modified n rank matrix is formed without matrix multiplication or extensive manipulation. Since the matrix has the same bandedness as the original eigensystems, it can be treated efficiently using the same banded equation solution algorithms that are used to find the eigenvectors.
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Cites
The algebraic eigenvalue problem
Wilkinson, J. H. (1965) · Cited by 5,833
The Algebraic Eigenvalue Problem
I., E., & Wilkinson, J. H. (1966) · Mathematics of Computation · doi:10.2307/2003558 · Cited by 5,140
Rates of change of eigenvalues and eigenvectors.
FOX, R. L., & KAPOOR, M. P. (1968) · AIAA Journal · doi:10.2514/3.5008 · Cited by 1,151
Handbook for Automatic Computation
Wilkinson, J. H., & Reinsch, C. (1971) · Springer eBooks · doi:10.1007/978-3-642-86940-2 · Cited by 545
Statistical Identification of Structures
COLLINS, J. D., HART, G. C., HASSELMAN, T. K., & KENNEDY, B. (1974) · AIAA Journal · doi:10.2514/3.49190 · Cited by 477
Handbook for Automatic Computation. Vol II, Linear Algebra
Bazilevsky, M. P., Wilkinson, J. H., & Reinsch, C. H. (1973) · Mathematics of Computation · doi:10.2307/2005673 · Cited by 187
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Computational methods in optimization considering uncertainties – An overview
Schuëller, G. I., & Jensen, H. A. (2008) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2008.05.004 · Cited by 572
Dealing with uncertainty in model updating for damage assessment: a review
Simoen, E., De Roeck, G., & Lombaert, G. (2015) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2014.11.001 · Cited by 540
Design sensitivity analysis: Overview and review
Tortorelli, D. A., & Michaleris, P. (1994) · Inverse Problems in Engineering · doi:10.1080/174159794088027573 · Cited by 437
Structural damage detection based on l 1 regularization using natural frequencies and mode shapes
Hou, R., Xia, Y., & Zhou, X. (2018) · Structural Control and Health Monitoring · doi:10.1002/stc.2107 · Cited by 127
Damage Identification in a Truss Tower by Regularized Model Updating
Weber, B., & Paultre, P. (2010) · Journal of Structural Engineering · doi:10.1061/(asce)st.1943-541x.0000105 · Cited by 54
Metadata
- Authors
- Nelson, R. B.
- Venue
- AIAA Journal
- Published
- 1976-09
- Volume
- 14
- Issue
- 9
- Pages
- 1201-1205
- ISSN
- 0001-1452 (ISSN-L)
- 1533-385X
- OpenAlex
- W2138395440
- Cited by
- 908
- References
- 6
- FWCI
- 2.15
- Type
- journal article
- Language
- en
- Open access
- closed
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