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Nonlinear Eigenvalue Problems with Specified Eigenvalues [PDF]
SIAM Journal on Matrix Analysis and Applications, 2014 This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T, we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed algebraic multiplicities.
Michael Karow +2 more
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The nonlinear eigenvalue problem [PDF]
Acta Numerica, 2017 Nonlinear eigenvalue problems arise in a variety of science and engineering applications, and in the past ten years there have been numerous breakthroughs in the development of numerical methods. This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a ...
Stefan Güttel, Françoise Tisseur
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Nonlinearizing Two-parameter Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications, 2021 We investigate a technique to transform a linear two-parameter eigenvalue problem, into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by considering it as a (standard) generalized eigenvalue problem. We characterize the equivalence between the original
Emil Ringh, Elias Jarlebring
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Poiseuille Flow with Couple Stresses Effect and No-slip Boundary Conditions [PDF]
Journal of Applied and Computational Mechanics, 2020 In this paper, the problem of Poiseuille flow with couple stresses effect in a fluid layer using the linear instability and nonlinear stability theories is analyzed.
Akil J. Harfash, Ghazi A. Meften
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Results in Applied Mathematics, 2020 The interior elastic transmission eigenvalue problem, arising from the inverse scattering theory of non-homogeneous elastic media, is nonlinear, non-self-adjoint and of fourth order.
Xia Ji, Peijun Li, Jiguang Sun
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A linear eigenvalue algorithm for the nonlinear eigenvalue problem [PDF]
Numerische Mathematik, 2012 A nonlinear matrix eigenvalue problem (NMEP) \(T(\lambda)x=0\) is transformed without loss of generality into a standard form \(\lambda B(\lambda)x=x\) (\(T\) and \(B\) analytic in \(\Omega\subset\mathbb{C}\)). This is then transformed into a linear operator eigenvalue problem (LOEP) of the form \(\lambda\mathcal{B}\varphi=\varphi\) (\(\varphi\in C_ ...
Elias Jarlebring +2 more
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Nonlinear elliptic equation with nonlocal integral boundary condition depending on two parameters
Mathematical Modelling and Analysis, 2022 In this paper, the two-dimensional nonlinear elliptic equation with the boundary integral condition depending on two parameters is solved by finite difference method.
Kristina Pupalaigė +2 more
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FEAST eigensolver for nonlinear eigenvalue problems [PDF]
Journal of Computational Science, 2018 The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors whose eigenvalues that are located inside some user-defined region in the complex plane. This makes it possible to parallelize the process of solving eigenvalue problems by simply dividing the complex plane ...
Brendan Gavin +2 more
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Numerical Analysis of Nonlinear Eigenvalue Problems [PDF]
Journal of Scientific Computing, 2010 We provide a priori error estimates for variational approximations of the ground state eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems of the form $-{div} (A\nabla u) + Vu + f(u^2) u = λu$, $\|u\|_{L^2}=1$. We focus in particular on the Fourier spectral approximation (for periodic problems) and on the $¶_1$ and $¶_2$ finite-element
Cancès, Eric +2 more
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Asymptotic Behavior of Solution to Nonlinear Eigenvalue Problem
Mathematics, 2020 We study the following nonlinear eigenvalue problem: −u″(t)=λf(u(t)),u(t)>0,t∈I:=(−1,1),u(±1)=0, where f(u)=log(1+u) and λ>0 is a parameter. Then λ is a continuous function of α>0, where α is the maximum norm α=∥uλ∥∞ of the solution uλ associated with λ.
Tetsutaro Shibata
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