Please use this identifier to cite or link to this item: https://doi.org/10.1137/120879841
Title: Computing derivatives of repeated eigenvalues and corresponding eigenvectors of quadratic eigenvalue problems
Authors: Qian, J.
Andrew, A.L.
Chu, D. 
Tan, R.C.E. 
Keywords: Derivatives of eigenvalues and eigenvectors
Multiple eigenvalues
Quadratic eigenvalue problems
Very close eigenvalues
Issue Date: 2013
Source: Qian, J., Andrew, A.L., Chu, D., Tan, R.C.E. (2013). Computing derivatives of repeated eigenvalues and corresponding eigenvectors of quadratic eigenvalue problems. SIAM Journal on Matrix Analysis and Applications 34 (3) : 1089-1111. ScholarBank@NUS Repository. https://doi.org/10.1137/120879841
Abstract: We consider quadratic eigenvalue problems in which the coefficient matrices, and hence the eigenvalues and eigenvectors, are functions of a real parameter. Our interest is in cases in which these functions remain differentiable when eigenvalues coincide. Many papers have been devoted to numerical methods for computing derivatives of eigenvalues and eigenvectors, but most require the eigenvalues to be well separated. The few that consider close or repeated eigenvalues place severe restrictions on the eigenvalue derivatives. We propose, analyze, and test new algorithm for computing first and higher order derivatives of eigenvalues and eigenvectors that are valid much more generally. Numerical results confirm the effectiveness of our methods for tightly clustered eigenvalues. Copyright © 2013 by SIAM.
Source Title: SIAM Journal on Matrix Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/103029
ISSN: 08954798
DOI: 10.1137/120879841
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