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Eigenvalue inclusion sets for linear response eigenvalue problems
Demonstratio Mathematica, 2022 In this article, some inclusion sets for eigenvalues of a matrix in the linear response eigenvalue problem (LREP) are established. It is proved that the inclusion sets are tighter than the Geršgorin-type sets.
He Jun, Liu Yanmin, Lv Wei
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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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Generalized eigenvalue problems with specified eigenvalues [PDF]
IMA Journal of Numerical Analysis, 2013 We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications.
D. Kressner +3 more
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Pareto Z-eigenvalue inclusion theorems for tensor eigenvalue complementarity problems
Journal of Inequalities and Applications, 2022 This paper presents some sharp Pareto Z-eigenvalue inclusion intervals and discusses the relationships among different Pareto Z-eigenvalue inclusion intervals for tensor eigenvalue complementarity problems.
Ping Yang +3 more
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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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Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations
Applied Mechanics, 2023 It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support.
László Kiss +2 more
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Rectangular eigenvalue problems
Advances in Computational Mathematics, 2022 AbstractOften the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m ≫ n collocation points. We show how eigenvalue problems can be solved in this setting by QR reduction to square matrix generalized eigenvalue problems.
Hashemi, B +2 more
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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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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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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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