Perturbation analysis for the eigenproblem of periodic matrix pairs
نویسنده
چکیده
This paper is devoted to perturbation analysis for the eigenproblem of periodic matrix pairs {(Aj ,Ej )}j=1. We first study perturbation expansions of periodic deflating subspaces and eigenvalue pairs. Then, we derive explicit expressions of condition numbers, perturbation bounds and backward errors for eigenvalue pairs and periodic deflating subspaces. © 2001 Elsevier Science Inc. All rights reserved.
منابع مشابه
Rayleigh-Ritz Approximation and Refinement of Periodic Matrix Pairs
In this paper, we study the Rayleigh-Ritz approximation for the eigenproblem of periodic matrix pairs. We show the convergence of the Ritz value and periodic Ritz vectors. Furthermore, we prove the convergence of refined periodic Ritz vectors and propose an efficient algorithm for computing the refined periodic Ritz vectors. The numerical result shows that the refinement procedure produces an e...
متن کاملDetermination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method
In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this...
متن کاملPerturbation of eigenvalues for periodic matrix pairs via the Bauer–Fike theorems
In earlier papers, the Bauer–Fike technique was applied to the ordinary eigenvalue problem Ax = λx, the generalized eigenvalue problem Ax = λBx and the matrix polynomial eigenvalue problem ∑m k=0 λAkx = 0. General multiple eigenvalues were dealt with and condition numbers were obtained for individual as well as clusters of eigenvalues. In this paper, we shall generalize the technique to the eig...
متن کاملStability Analysis of a Strongly Displacement Time-Delayed Duffing Oscillator Using Multiple Scales Homotopy Perturbation Method
In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...
متن کاملNonlinear Vibration Analysis of the Composite Cable using Perturbation Method and the Green-Lagrangian Nonlinear Strain
In this study, nonlinear vibration of a composite cable is investigated by considering nonlinear stress-strain relations. The composite cable is composed of an aluminum wire as reinforcement and a rubber coating as matrix. The nonlinear governing equations of motion are derived about to an initial curve and based on the fundamentals of continuum mechanics and the nonlinear Green-Lagrangian stra...
متن کامل