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Guaranteed Eigenvalue Bounds for the Steklov Eigenvalue Problem [PDF]

open access: yesSIAM Journal on Numerical Analysis, 2019
To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive definiteness of bilinear forms in the formulation of eigenvalue problems.
Hehu Xie, Xuefeng Liu
exaly   +4 more sources
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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
openaire   +1 more source

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
openaire   +1 more source

Product Eigenvalue Problems [PDF]

open access: yesSIAM Review, 2005
Summary: Many eigenvalue problems are most naturally viewed as product eigenvalue problems. The eigenvalues of a matrix \(A\) are wanted, but \(A\) is not given explicitly. Instead it is presented as a product of several factors: \(A = A_{k}A_{k-1}\dots A_{1}\). Usually more accurate results are obtained by working with the factors rather than forming \
David S Watkins
exaly   +3 more sources

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