Results 11 to 20 of about 12,585,660 (209)
The Quadratic Eigenvalue Problem [PDF]
SIAM Review, 2001 The authors review current knowledge of the matrix quadratic eigenvalue problem, \[ (\lambda ^2 M+\lambda C+K)x=0, \qquad y^* (\lambda ^2 M+\lambda C+K)=0, \tag{1} \] including its main applications and its numerical solution, and give an excellent guide to the literature.
Françoise Tisseur, Karl Meerbergen
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Automatic rational approximation and linearization of nonlinear eigenvalue problems [PDF]
IMA Journal of Numerical Analysis, 2018 We present a method for solving nonlinear eigenvalue problems (NEPs) using rational approximation. The method uses the Antoulas–Anderson algorithm (AAA) of Nakatsukasa, Sète and Trefethen to approximate the NEP via a rational eigenvalue problem.
Pieter Lietaert +3 more
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Deep convolutional neural networks for eigenvalue problems in mechanics [PDF]
International Journal for Numerical Methods in Engineering, 2018 We show that deep convolutional neural networks (CNNs) can massively outperform traditional densely connected neural networks (NNs) (both deep or shallow) in predicting eigenvalue problems in mechanics.
D. Finol +3 more
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Fractional eigenvalue problems on $\mathbb{R}^N$
Electronic Journal of Qualitative Theory of Differential Equations, 2020 Let $N\geq 2$ be an integer. For each real number $s\in(0,1)$ we denote by $(-\Delta)^s$ the corresponding fractional Laplace operator. First, we investigate the eigenvalue problem $(-\Delta)^s u=\lambda V(x)u$ on $\mathbb{R}^N$, where $V:\mathbb{R}^N ...
Andrei Grecu
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Fractional Sturm–Liouville Eigenvalue Problems, II
Fractal and Fractional, 2022 We continue the study of a non-self-adjoint fractional three-term Sturm–Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left Riemann–Liouville fractional integral under Dirichlet type boundary ...
Mohammad Dehghan, Angelo B. Mingarelli
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The nonconforming Virtual Element Method for eigenvalue problems [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2018 We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same formulation the two- and three-dimensional case.
F. Gardini, G. Manzini, G. Vacca
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A constrained eigenvalue problem [PDF]
Linear Algebra and its Applications, 1989 For the problem of finding \(Min(x^ TAx)\) for a symmetric matrix A subject to \(x^ Tx=1\) and \(N^ Tx=t\) theoretical and numerical methods are described. First the linear constraint is removed and then Lagrange multipliers are employed reducing the problem to solve either a secular equation or a quadratic eigenvalue problem.
Gander, Walter +2 more
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FEAST Eigensolver for Nonlinear Eigenvalue Problems [PDF]
Journal of Computer 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.
Brendan Gavin, A. Miedlar, E. Polizzi
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Structured Eigenvalue Problems [PDF]
GAMM-Mitteilungen, 2006 AbstractMost eigenvalue problems arising in practice are known to be structured. Structure is often introduced by discretization and linearization techniques but may also be a consequence of properties induced by the original problem. Preserving this structure can help preserve physically relevant symmetries in the eigenvalues of the matrix and may ...
Fassbender, Heike, Kressner, Daniel
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Sensitivity analysis of waveguide eigenvalue problems [PDF]
Advances in Radio Science, 2011 We analyze the sensitivity of dielectric waveguides with respect to design parameters such as permittivity values or simple geometric dependencies. Based on a discretization using the Finite Integration Technique the eigenvalue problem for the wave ...
N. Burschäpers +3 more
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