Results 271 to 280 of about 157,300 (313)
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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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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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On Eigenvalues and Annealing Rates
Mathematics of Operations Research, 1988We evaluate asymptotically the eigenvalues of transition rate matrices (Qijϵ)i,j=1n with Qijϵ ∼ exp(−(U(j) − U(i))+/ϵ) for some function U using Ventcel's graphic method. As a consequence, we can compare the “nearly optimal” annealing rate in (Gidas, B. 1985. Global optimization via the Langevin equation. Proc. 24th IEEE Conf. Decision and Control, Ft.
Tzuu-Shuh Chiang, Yunshyong Chow
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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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SIAM Journal on Matrix Analysis and Applications, 1999
A new algorithm for computing the eigenvalues of a narrow-band, nearly tridiagonal upper Hessenberg matrix is introduced. The method called BR algorithm belongs to the family of the QR algorithms. The new method works well in conjuction with the look-ahead Lanczos process: it attempts to exploit and preserve the structure of the auxiliary matrix ...
Geist, G. A. +2 more
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A new algorithm for computing the eigenvalues of a narrow-band, nearly tridiagonal upper Hessenberg matrix is introduced. The method called BR algorithm belongs to the family of the QR algorithms. The new method works well in conjuction with the look-ahead Lanczos process: it attempts to exploit and preserve the structure of the auxiliary matrix ...
Geist, G. A. +2 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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Isoperimetric Inequalities and Eigenvalues
SIAM Journal on Discrete Mathematics, 1997Summary: An upper bound is given on the minimum distance between \(i\) subsets of same size of a regular graph in terms of the \(i\)th largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the \(i\)th largest eigenvalue for any integer \(i\). Our bounds are shown to be asymptotically tight for explicit families of graphs
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