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Principal Eigenvalues for some Quasilinear Elliptic Equations on IRN
, 1997 Stavrakakis, N +2 more
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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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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, 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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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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Bulletin of the London Mathematical Society, 1985
The author proves that an \(n\times n\) matrix A with quaternion entries has a quaternion eigenvalue \(\lambda\) in the sense that \(\lambda\) I-A fails to be invertible.
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The author proves that an \(n\times n\) matrix A with quaternion entries has a quaternion eigenvalue \(\lambda\) in the sense that \(\lambda\) I-A fails to be invertible.
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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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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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2007
Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
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Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
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