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Relative Perturbation Theory for Quadratic Eigenvalue Problems [PDF]
, 2016 In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form $\lambda^2 M x + \lambda C x + K x = 0$, where $M$ and $K$ are nonsingular Hermitian matrices and $C$ is a ...
Benner, Peter +3 more
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Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems
Shock and Vibration, 2018 Dynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed.
Philip D. Cha, Austin Shin
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Perturbations of symmetric eigenvalue problems
Applied Mathematics Letters, 2002 AbstractBy use of a cut-off technique, we obtain a result of multiple solutions to perturbations of symmetric eigenvalue problems with constraint such as — Δu = λ(f(x, u)+εg(x, u)) in Ω, u|∂Ω = 0, ∫Ω |∇ u|2 dx = r2.
Yongqing Li, Zhaoli Liu
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The Fréchet Derivative of an Analytic Function of a Bounded Operator with Some Applications
International Journal of Mathematics and Mathematical Sciences, 2009 The main result in this paper is the determination of the Fréchet derivative of an analytic function of a bounded operator, tangentially to the space of all bounded operators. Some applied problems from statistics and numerical analysis are included as a
D. S. Gilliam +3 more
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Principal Eigenvalues and Perturbation
, 1995 In a classical article, Hess and Kato [HK] study the problem $$\left\{ {\begin{array}{*{20}{c}} {Au + \lambda mu = 0} \\ {0 \leqslant u \in D\left( A \right), u \ne 0,} \end{array}} \right.$$ (0.1) where A is a strongly elliptic operator on a bounded open set Ω of R n with Dirichlet boundary conditions and m is a continuous bounded function ...
Arendt, W, Batty, C
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Fragmentation of a dynamically condensing radiative layer [PDF]
, 2009 In this paper, the stability of a dynamically condensing radiative gas layer is investigated by linear analysis. Our own time-dependent, self-similar solutions describing a dynamical condensing radiative gas layer are used as an unperturbed state.
Iwasaki, Kazunari, Tsuribe, Toru
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Boundary Value Problems, 2010 We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both ...
R. Darzi, A. Neamaty
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Closed form bound-state perturbation theory
International Journal of Mathematics and Mathematical Sciences, 1980 The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the
Ollie J. Rose, Carl G. Adler
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On Eigenvalues and Eigenvectors of Perturbed [PDF]
ITB Journal of Sciences, 2009 This work studied eigenvalues and eigenvectors of a class of perturbed pairwise comparison matrices (PCMs). This type of matrices arises from Analytical Hierarchical Process with inconsistency comparison. By employing some nice structures of the PCMs, we show that the object dimension of size n ≥ 3 can be reduced into a case of size 3, hence simplify
A. D. Garnadi, Pudji Astuti
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Journal of Materials and Engineering Structures, 2022 This paper deal with the stochastic finite element method for investigating the eigenvalues of free vibration of non-uniform beams due to a random field of elastic modulus.
Nhung Thi NGUYEN +3 more
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