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On the higher eigenvalues for the $\infty$ -eigenvalue problem
Calculus of Variations and Partial Differential Equations, 2005The authors consider a nonlinear eigenvalue problem associated with a limiting version of the \(p\)-Laplacian for \(p=\infty\). Namely, if \(\Omega\) is an open subset of \(\mathbb R^n\), \(S_{n\times n}\) is the set of \(n\times n\) real symmetric matrices with real entries, the authors consider the nonlinear problem \( F_{\Lambda}(u,Du,D^2u)=0\) in \(
Juutinen, Petri, Lindqvist, Peter
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Dependence of Eigenvalues on the Problem
Mathematische Nachrichten, 1997AbstractThe eigenvalues of linear, regular, two point boundary value problems depend continuously on the problem. In the important self‐adjoint case studied by Naimark and Weidmann this dependence is differentiable and the derivatives of the eigenvalues with respect to a given parameter: an endpoint, a boundary condition, a coefficient, or the weight ...
Kong, Q., Wu, H., Zettl, A.
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SIAM Review, 1998
In the inverse eigenvalue problem, one has to construct a matrix with a (partially) given spectrum. The problem appears in many different forms and in many different applications. Usually the problem is constrained in the sense that the matrix \(M\) that one wants to find has to be in a certain class. For example it should be of the form \(M=A+X\) or \(
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In the inverse eigenvalue problem, one has to construct a matrix with a (partially) given spectrum. The problem appears in many different forms and in many different applications. Usually the problem is constrained in the sense that the matrix \(M\) that one wants to find has to be in a certain class. For example it should be of the form \(M=A+X\) or \(
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On a controlled eigenvalue problem
Systems & Control Letters, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anup Biswas, Vivek S. Borkar
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On a Quadratic Eigenvalue Problem
SIAM Journal on Mathematical Analysis, 1974It is shown that the eigenvalue problem $u'' + Bu(\lambda ^2 + \lambda p)u$; $u(0) = u(1) = 0$ (where p is a positive function and B an arbitrary bounded operator on $L^2 [0,1]$ possesses in general two different sets of eigenfunctions, each of which is an unconditional basis for $L^2$ and other spaces.
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Explorations in Numerical Analysis, 2021
R. Gilbert, G. C. Hsiao, R. Ronkese
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R. Gilbert, G. C. Hsiao, R. Ronkese
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Computation of Selected Eigenvalues of Generalized Eigenvalue Problems
Journal of Computational Physics, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nayar, Narinder, Ortega, James M.
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On the computation of all eigenvalues for the eigenvalue complementarity problem
Journal of Global Optimization, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luís M. Fernandes +3 more
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A note on unimodular eigenvalues for palindromic eigenvalue problems
International Journal of Computer Mathematics, 2012We consider the occurrence of unimodular eigenvalues for palindromic eigenvalue problems associated with the matrix polynomial where A i *= A n − i with M * ≡ M T, M H or . From the properties of palindromic eigenvalues and their characteristic polynomials, we show that eigenvalues are not generically excluded from the unit circle, thus
Chun-Yueh Chiang +2 more
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The Interval Eigenvalue Problem
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1991Let \(A^ I\) be a quadratic interval matrix over \(R\). Then \(\lambda\in C\) is called an eigenvalue of \(A^ I\), if there exists a matrix \(A\in A^ I\) and a vector \(x\neq 0\) such that \(Ax=\lambda x\). The paper is concerned with the set of eigenvalues of \(A^ I\), especially with bounds for them. The symmetric case is discussed first, and is then
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