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Perturbation theory of eigenvalue problems
Franz Rellich,B. J. Berkowitz +1 more
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The article was published on 1969-01-01 and is currently open access. It has received 600 citations till now. The article focuses on the topics: Inverse iteration & Eigenvalue perturbation.read more
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Strong Semismoothness of Eigenvalues of Symmetric Matrices and Its Application to Inverse Eigenvalue Problems
Defeng Sun,Jie Sun +1 more
TL;DR: It is proved in this paper that the eigenvalues of a symmetric matrix are strongly semismooth everywhere and can be used to analyze the quadratic convergence of Newton's method for solving inverse eigenvalue problems (IEPs) and generalized IEPs with multiple eigen values.
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Fifty years of eigenvalue perturbation theory
TL;DR: In this article, the authors highlight progres in the study of eigenvalue perturbation theory, especially problems connected to quantum mechanics, and discuss six models: isoelectronic atoms, autoionizing states, the anharmonic oscillator, double wells, and the Zeeman and Strak effects.
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Dynamics for Modal Interpretations
TL;DR: In this paper, a general framework for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks, has been developed, which admits many empirically equivalent dynamics.
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Variational and perturbative schemes for a spiked harmonic oscillator
TL;DR: In this paper, a variational analysis of the spiked harmonic oscillator Hamiltonian operator is presented, where α is a real positive parameter, and the eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter.
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Remarks on virtual bound states for semi—bounded operators
TL;DR: In this article, the number of bound states appearing below the spectrum of a semi-bounded operator in the case of a weak, indefinite perturbation was calculated for a single operator.