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On Eigenvalue Optimization [PDF]
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, Michael K. H. Fan
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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 \(
Peter Lindqvist, Petri Juutinen
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1986
Recall that an n × n matrix B is similar to an n × n matrix A if there is an invertible n × n matrix P such that B = P −1 AP. Our objective now is to determine under what conditions an n × n matrix is similar to a diagonal matrix. In so doing we shall draw together all of the notions that have been previously developed.
T. S. Blyth, Edmund F. Robertson
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Recall that an n × n matrix B is similar to an n × n matrix A if there is an invertible n × n matrix P such that B = P −1 AP. Our objective now is to determine under what conditions an n × n matrix is similar to a diagonal matrix. In so doing we shall draw together all of the notions that have been previously developed.
T. S. Blyth, Edmund F. Robertson
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The Distribution of the Eigenvalues
1991It follows from the results of Chapter 3 that if the function q(x) of the Sturm-Liouville operator $$ {L_y} = - y'' + q(x)y,\,a < x < , $$ (1.1) is bounded from below, and tends to +∞ as x → a or x → b (or both), then the spectrum of L is discrete (assuming that at least one of the endpoints is singular; furthermore, if at least one of them ...
B. M. Levitan, I. S. Sargsjan
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1966
Publisher Summary This chapter focuses on eigenvalue problems. Eigenvalue problems arise in a number of different areas of mathematics. The differential equation and the boundary conditions constitute an eigenvalue problem. In an eigenvalue problem, associated with a linear homogeneous differential equation of arbitrary order n, each linear ...
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Publisher Summary This chapter focuses on eigenvalue problems. Eigenvalue problems arise in a number of different areas of mathematics. The differential equation and the boundary conditions constitute an eigenvalue problem. In an eigenvalue problem, associated with a linear homogeneous differential equation of arbitrary order n, each linear ...
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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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THE DISTRIBUTION OF THE EIGENVALUES IN CERTAIN EIGENVALUE PROBLEMS
The Quarterly Journal of Mathematics, 1964openaire +2 more sources