Journal ArticleDOI
Simplified calculation of eigenvector derivatives
Reads0
Chats0
TLDR
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.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.read more
Citations
More filters
Journal ArticleDOI
An eigenspace method for computing derivatives of semi-simple eigenvalues and corresponding eigenvectors of quadratic eigenvalue problems
Xin Lu,Shu-fang Xu +1 more
TL;DR: This paper proposes a new method for computing derivatives of semi-simple eigenvalues and corresponding eigenvectors of the quadratic matrix polynomial, where the condition number of the coefficient matrix is the ratio of the maximum singular value to the minimum nonzero singular value of Q.
Efficient Computation of Eigenvector Sensitivities for Structural Dynamics via Conjugate Gradients
TL;DR: In this paper, an iterative procedure is presented for computing eigenvector sensitivities due to finite element model parameter variations, which is a Preconditioned Conjugate Projected Gradient-based technique and is intended to utilize the existing matrix factorizations developed for an iteration eigensolution such as Lanczos or Subspace Iteration.
Journal ArticleDOI
New theoretical developments on eigenvector derivatives with repeated eigenvalues
Rongming Lin,Teng Yong Ng +1 more
TL;DR: A concept of global design variable is developed in which all intended multivariate design modifications are grouped into a single global variable to which eigenvector derivatives are derived, rendering real major applications of the proposed method to the predictions of structural design modifications.
Journal ArticleDOI
Sensitivity derivatives of eigendata of one-dimensional structural systems
TL;DR: In this paper, a general formulation based on the transfer matrix is presented to calculate the sensitivity derivatives of eigenvalue problems of one-dimensional structural systems, which is equally applicable to any discrete or distributed system of one variable.
Journal ArticleDOI
Second-Order Sensitivity of Smart Structures
Xiaojian Liu,David Begg +1 more
TL;DR: A second-order sensitivity analysis for a smart structural system formulated in terms of multiobjective optimization where structural design variables and control parameters are equally treated as design variables is presented in this paper.
References
More filters
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
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
Statistical Identification of Structures
TL;DR: In this paper, a method is formulated for systematically using experimental measurements of the natural frequencies and mode shapes of a structure to modify stiffness and mass characteristics of a finite element model, and an additional feature is that the engineer's confidence in the modeling of the various finite elements is quantified and incorporated into the revision procedure.
Journal ArticleDOI
Handbook for Automatic Computation. Vol II, Linear Algebra
James Hardy Wilkinson,C. Reinsch +1 more
TL;DR: Haida gwaii tourism guide, Handbook of raman spectroscopy, and the Jordan form, Kronecker's form for matrix pencils, and various condition in the Handbook.