Journal ArticleDOI
Derivatives of complex eigenvectors with distinct and repeated eigenvalues
Zhonghai Xu,Baisheng Wu +1 more
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TLDR
In this article, the first-order derivatives of complex eigenvectors for general non-defective eigensystems have been investigated and a new normalization condition is proposed, with which they can compute unique firstorder derivatives.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 © 2007 John Wiley & Sons, Ltd.read more
Citations
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A parallel way for computing eigenvector sensitivity of asymmetric damped systems with distinct and repeated eigenvalues
Li Li,Yujin Hu,Xuelin Wang +2 more
TL;DR: The aim of this paper is to show how to compute the left and right eigenvector derivatives separately and independently such that those can be computed in a parallel way and the calculation of eigenvalue sensitivity of N damped asymmetric systems with repeated eigenvalues is derived.
Journal ArticleDOI
A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives
TL;DR: Major important applications of eigenderivatives to finite element model updating, structural design and modification prediction, performance optimization of structures and systems, optimal control system design, damage detection and fault diagnosis, as well as turbine bladed disk vibrations are examined.
Journal ArticleDOI
A study on design sensitivity analysis for general nonlinear eigenproblems
Li Li,Yujin Hu,Xuelin Wang +2 more
TL;DR: In this article, the design sensitivity analysis for the general nonlinear eigenproblem with respect to arbitrary design parameters is studied, and the derivatives of eigensolutions can be treated in a unified way for different structural systems (i.e., undamped systems, viscously and nonviscously damped systems and nonlinear systems).
Journal ArticleDOI
Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues
TL;DR: A combined normalization, which combines two traditional normalizations, is presented and a method for sensitivity analysis of eigenvalues and eigenvectors is studied, which can determine the eigenvector derivatives directly and is robust since the components of coefficient matrices are all of the same order of magnitude.
Journal ArticleDOI
Derivatives of spin dynamics simulations
TL;DR: In this article, analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters are described. But the methods described are significantly faster, more accurate, and more reliable than the finite difference approximations typically employed.
References
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Journal ArticleDOI
Rates of change of eigenvalues and eigenvectors.
R. L. Fox,M. P. Kapoor +1 more
TL;DR: Exact expressions for rates of change of eigenvalues and eigenvector to facilitate computerized design of complex structures are presented.
Journal ArticleDOI
Simplified calculation of eigenvector derivatives
TL;DR: A simplified procedure is presented for the determination of the derivatives of eigenvectors of nth order algebraic eigensystems, applicable to symmetric or nonsymmetric systems, and requires knowledge of only one eigenvalue and its associated right and left eigenavectors.
Journal ArticleDOI
Sensitivity Analysis of Discrete Structural Systems
TL;DR: In this paper, a survey of sensitivity derivatives for discrete structural systems is presented, primarily focusing on publications developed in nonstructural fields such as electronics, control, and physical chemistry which are directly applicable to structural problems.
Journal ArticleDOI
Eigenvector derivatives with repeated eigenvalues
TL;DR: The algorithm preserves the symmetry and band structure of the matrices, allowing efficient computer storage and solution techniques, and applications include sensitivity analysis and optimization of the normal modes of finite-element modeled structures, such as large space structures.