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On Eigenvalue Optimization

SIAM Journal on Optimization, 1995
Summary: We study optimization problems involving eigenvalues of symmetric matrices. One of the difficulties with numerical analysis of such problems is that the eigenvalues, considered as functions of a symmetric matrix, are not differentiable at those points where they coalesce. We present a general framework for a smooth (differentiable) approach to
Alexander Shapiro 0001   +1 more
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On the higher eigenvalues for the $\infty$ -eigenvalue problem

Calculus of Variations and Partial Differential Equations, 2005
The 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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Computation of Selected Eigenvalues of Generalized Eigenvalue Problems

Journal of Computational Physics, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nayar, Narinder, Ortega, James M.
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A note on unimodular eigenvalues for palindromic eigenvalue problems

International Journal of Computer Mathematics, 2012
We 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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On the computation of all eigenvalues for the eigenvalue complementarity problem

Journal of Global Optimization, 2014
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Luís M. Fernandes   +3 more
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