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The Minimum Ratio of Two Eigenvalues
SIAM Journal on Applied Mathematics, 1976The first two eigenvalues, $\lambda _1 $ and $\lambda _2 $, of the problem $y'' + \lambda \phi ( x )y = 0$, $y( { \pm \frac{1}{2}} ) = 0$ are considered. The minimum of their ratio ${\lambda _2 / \lambda _1 }$ is sought for $\phi ( x )$ ranging over the class of piecewise continuous functions satisfying the inequalities $0 < a \leqslant \phi ( x ...
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1992
Abstract : For over one hundred years, the eigenvalue problem has been investigated by mathematicians, physicists, and engineers. Scientists explored the characterization, location, perturbation and computation of eigenvalues, to name a few topics. This thesis is devoted to the separation of eigenvalues. We will find the minimum gap between eigenvalues
Tzon-Tzer Lu, Beresford Parlett
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Abstract : For over one hundred years, the eigenvalue problem has been investigated by mathematicians, physicists, and engineers. Scientists explored the characterization, location, perturbation and computation of eigenvalues, to name a few topics. This thesis is devoted to the separation of eigenvalues. We will find the minimum gap between eigenvalues
Tzon-Tzer Lu, Beresford Parlett
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On the minimum eigenvalue gap for vibrating string
Journal of Mathematical Analysis and Applications, 2022Consider a Sturm-Liouville problem with Dirichlet type boundary conditions (BCs). To speak more precise consider the differential equation \[ y'' +\lambda \rho(x) y=0 \] with BCs \[ y(0)=y(1)=0. \] As we know \(\rho(x)\) is called the density function and describes the mass distribution of a string.
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Lower Bounds for the Minimum Eigenvalue of the bi-Laplacian on a Graph
Differential EquationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kulaev, R. Ch., Karkuzaev, S. A.
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Approximation Guarantees for the Minimum Linear Arrangement Problem by Higher Eigenvalues
ACM Transactions on Algorithms, 2012Given an n -vertex undirected graph G = ( V , E ) and positive edge weights { w e } e∈E , a linear arrangement is a permutation π : V → {1, 2, …,
Suguru Tamaki, Yuichi Yoshida
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Minimum Properties of Eigenvalues — Elementary Proofs
1980The purpose of this paper is to use an elementary integral inequality and some simple linear algebra to give a completely elementary proof of the minimum properties of all eigenvalues of Sturm-Liouville problems. The results are a simplification of work published in [1], where singular cases were considered but general boundary conditions were not.
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On the minimum eigenvalue of the fan product
Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2023Qin Zhong, Ling Li
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Pole assignment with optimality and minimum eigenvalue sensitivity
Proceedings of the Institution of Electrical Engineers, 1975A method is presented for designing a constant-gain feedback controller for assigning the closed-loop poles of a linear system to specified locations while minimising an objective functional which is a linear combination of a quadratic performance index and an eigenvalue sensitivity functional.
K. Ramar, V. Gourishankar
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Principal-Minimum Eigenvalue Algorithm for Signal Sensing
2023 IEEE 23rd International Conference on Communication Technology (ICCT), 2023Yumin Zhong, Yanhua Li
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An Asymptotic Formula for the Minimum Eigenvalues of Hilbert Type Matrices
Functional Analysis and Its Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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