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Derivatives of complex eigenvectors with distinct and repeated eigenvalues

✍ Scribed by Zhonghai Xu; Baisheng Wu

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
165 KB
Volume
75
Category
Article
ISSN
0029-5981

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✦ Synopsis

Abstract

In this paper, we investigate the computation of the first‐order derivatives of complex eigenvectors for general non‐defective eigensystems. A new normalization condition is proposed, with which we can compute unique first‐order derivatives of arbitrary differentiable eigenvectors of systems with distinct and repeated eigenvalues. We also present an efficient algorithm to compute the particular solutions to the governing equations of the first‐order derivatives of eigenvectors. Finally, numerical examples are included to demonstrate the validity of the proposed method. Copyright Β© 2007 John Wiley & Sons, Ltd.

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A new simultaneous iteration method is presented for computing mixed second-order partial derivatives of several eigenvalues and the corresponding eigenvectors of a matrix which depends smoothly on some realvalued design parameters. Numerical results illustrate the viability of the method, and show