2 edition of Application of eigenvalue sensitivity and eigenvector sensitivity in eigencomputations found in the catalog.
Written in English
|Statement||by Purandar Sarmah|
|The Physical Object|
|Pagination||vi, 115 leaves :|
|Number of Pages||115|
eigenvalues and the eigenvectors are affected by changes in the parameters. This subject is of great importance in the optimization of structural dynamics and control system design. For background on sensitivity analysis and its applications see the book by H_aug, Choi, and Komkov (). Eigenvectors and eigenvalues are used widely in science and engineering. They have many applications, particularly in physics. Consider rigid physical bodies.
Abstract: Traditional eigenvalue sensitivity studies of power systems require the formulation of the system matrix, which lacks sparsity. A new sensitivity analysis approach, derived for a sparse formulation, is presented. Variables that are computed as intermediate results in established eigenvalue programs for power systems, but not used further, are given a new interpretation. Originally utilized to study principal axes of the rotational motion of rigid bodies, eigenvalues and eigenvectors have a wide range of applications, for example in stability analysis, vibration analysis, atomic orbitals, facial recognition, and matrix diagonalization.
eigenvalues of A = a h h b ¸ and constructs a rotation matrix P such that PtAP is diagonal. As noted above, if λ is an eigenvalue of an n × n matrix A, with corresponding eigenvector X, then (A − λIn)X = 0, with X 6= 0, so det(A−λIn) = 0 and there are at most n distinct eigenvalues of A. Please note that much of the Application Center contains content submitted directly from members of our user community. Although we do our best to monitor for objectionable content, it is possible that we occasionally miss something.
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APPLICATION OF EIGENVALUE SENSITIVITY AND EIGENVECTOR SENSITIVITY IN EIGENCOMPUTATIONS By PURANDAR SARMAH December Chairman: William Hager Major Department: Mathematics Inin his paper "Bidiagonalization and Diagonalization," William W Hager presented an algorithm to diagonalize a matrix with distinct eigenvalues.
ment the. Application of eigenvalue sensitivity and eigenvector sensitivity in eigencomputations. By Purandar Sarmah. Abstract (Thesis) Thesis (Ph. D.)--University of Florida, (Bibliography) Includes bibliographical references (leaves )(Statement of Responsibility) by Author: Purandar Sarmah.
Simplo and explicit derivations arc given of expressions for the eigenvalue and eigenvector sensitivity coefficients for the fundamental eigenproblem associated with tho behaviour of linear systems governed by equations of the form x = expressions relating changes in the eigenvalues and eigenvectors of tho matrix A to changes in A have been given by numerous Cited by: Abstract.
The utility of complex perturbations to estimate the sensitivity of modal parameters in self-adjoint conservative models is examined. In the Complex Step Derivative (CSD) approach the parameter for which the derivative is required is perturbed in the direction of the imaginary axis and the eigenvalue problem for the perturbed matrices is solved; the real part has the solution of the Cited by: 6.
The application of eigenvalues and eigenvectors is useful for decoupling three-phase systems through symmetrical component transformation. Size: 64KB. proposed for accurate and efficient computation of these sensitivity coefficients .
These methods compute eigenvalue sensitivities in the same way, but differ in their techniques for eigenvector sensi tivities.
The present work presents an improvement of the existing methods for problems with distinct roots; the problem of repeated. This paper proposes a new method of eigenvector-sensitivity analysis for real symmetric systems with repeated eigenvalues and eigenvalue derivatives. The derivation is completed by using information from the second and third derivatives of the eigenproblem, and is applicable to the case of repeated eigenvalue derivatives.
The method is employed to analyze in detail a transcendental eigenvalue problem arising in the analysis of a bridge deck subjected to aerodynamic forces.
The sensitivities of eigenvalues and eigenvectors are successfully used to improve the performance of an iterative method used for solving the eigenvalue. () An eigenspace method for computing derivatives of semi-simple eigenvalues and corresponding eigenvectors of quadratic eigenvalue problems.
Applied Numerical Mathemat () Rounding errors of partial derivatives of simple eigenvalues of the quadratic eigenvalue. 20 Some Properties of Eigenvalues and Eigenvectors We will continue the discussion on properties of eigenvalues and eigenvectors from Section Throughout the present lecture A denotes an n× n matrix with real entries.
We recall that a nonvanishing vector v is said to be an eigenvector if there is a scalar λ, such that Av = λv. (1).
Eigenvalue Jacobian and a Related Application Jacobian of eigenvalue vector is obtained by repeated application of the method (" EigenSensitivity"). A more efficient version may be obtained by identifying the repeated multiplications and/or common factors.
Abhinav Kumar Singh, Bikash C. Pal, in Dynamic Estimation and Control of Power Systems, Eigenvalues. An eigenvalue of a dynamic system which can be represented in form of () is defined as a root of the equation (A − λ I) = λ i is the ith eigenvalue of the system, then the right eigenvector, r i, and the left eigenvector, l i, corresponding to λ i are given by the.
Dissertation: Application of Eigenvalue Sensitivity and Eigenvector Sensitivity in Eigencomputations. Advisor: William Ward Hager.
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Lecture Some Properties of Eigenvalues and Eigenvector We will continue the discussion on properties of eigenvalues and eigenvectors from Lecture Throughout the present lecture A denotes an n × n matrix with real entries. A vector v, diﬀerent from the zero-vector, is said to be an eigenvector if there is a scalar λ, such that Av.
Computation of eigenvalues and eigenvectors of matrices is a major task in Numerical Linear Alegbra and the sensitivity analysis of eigenvalues plays an important role in the accuracyassessment of computed eigenvalues [14, 17, 6]. Sensitivity Analysis of the Eigenvalue Problem for General Dynamic Systems with Application to Bridge Deck Flutter.
The sensitivities of eigenvalues and eigenvectors are successfully used to improve the performance of an iterative method used for solving the eigenvalue problem.
proceedings papers, and available book chapters across the. Eigenvalue and eigenvector derivatives of second-order systems using structure-preserving equivalences Journal of Sound and Vibration, Vol.No.
An experiment-based frequency sensitivity enhancing control approach for structural damage detection. For d = 2 we have 0s1 =o- 8. Conclusions The formulae for derivatives of eigenvalues and eigenvectors of linear, time invariant, parameterized descriptor systems were derived.
The presented approach gives insight into the problem of eigenvalue- eigenvector sensitivity, especially highlighting the influence of system eigenstructure. Why are eigenvalues and eigenvectors important. Let's look at some real life applications of the use of eigenvalues and eigenvectors in science, engineering and computer science.
Google's PageRank. Google's extraordinary success as a search engine was due to their clever use of eigenvalues and eigenvectors. From the time it was introduced in. We present a general framework for the sensitivity and backward perturbation analysis of linear as well as nonlinear multiparameter eigenvalue problems (MEPs).
For a general norm on the space of MEPs, we present a comprehensive analysis of the sensitivity of simple eigenvalues of.
Eigenvalue sensitivity example. In this example, we construct a matrix whose eigenvalues are moderately sensitive to perturbations and then analyze that sensitivity. We begin with the statement B = which produces B = 3. 0. 7. 0. 2. 0. 0. 0. 1. Obviously, the eigenvalues .Get this from a library!
Investigation, development, and application of optimal output feedback theory. Volume IV, Measure of Eigenvalue/Eigenvector sensitivity to system parameters and unmodeled dynamics.
[Nesim Halyo; United States. National Aeronautics and Space Administration. Scientific and Technical Information Division.].Let us say A is an “n × n” matrix and λ is an eigenvalue of matrix A, then X, a non-zero vector, is called as eigenvector if it satisfies the given below expression; AX = λX.
X is an eigenvector of A corresponding to eigenvalue, λ. Note: There could be infinitely many Eigenvectors, corresponding to one eigenvalue.