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Bounds for the minimum eigenvalue of a symmetric Toeplitz matrix
1998In a recent paper Melman [12] derived upper bounds for the smallest eigenvalue of a real symmetric Toeplitz matrix in terms of the smallest roots of rational and polynomial approximations of the secular equation $f(lambda)=0$, the best of which being constructed by the $(1,2)$-Pad{accent19 e} approximation of $f$. In this paper we prove that this bound
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MINIMUM WEIGHT MEMBERS FOR GIVEN LOWER BOUNDS ON EIGENVALUES
Engineering Optimization, 1981The problem is solved of minimizing the mass of an elastic bar whose Euler buckling load and fundamental frequency of transverse vibrations are larger than certain prescribed values. The bar has a solid cross section and is to perform natural vibrations or act as a column at different times during its design life.
R. D. Parbery, Bhushan Lal Karihaloo
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Enhanced Maximum-Minimum Eigenvalue Based Spectrum Sensing
2019 International Conference on Information and Communication Technology Convergence (ICTC), 2019The maximum eigenvalue captures the signal correlation well, and the minimum eigenvalue also captures the noise characteristics well, thus the spectrum sensing algorithm based on the maximum and minimum eigenvalue gets better detection performance.
Wenjing Zhao +3 more
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Improving Minimum-Variance Portfolios by Alleviating Overdispersion of Eigenvalues
Journal of Financial and Quantitative Analysis, 2019In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. Yet the eigenvalues of the sample covariance matrix are often overdispersed, leading to severe estimation errors in the inverse covariance matrix.
Fangquan Shi +3 more
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The eigenvalue problem as a form of minimum least-squared approximation
Ocean Engineering, 1992Abstract Two important tools used in the interpretation of ocean engineering data are the Minimum Least-Squared approximation technique (MLS) and the spectral analysis technique. Often, the inherent assumptions in these analytical techniques are overlooked by users which may, at times, bias the picture of the physics that remains to be understood ...
Rao Tatavarti, Y. Andrade
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Upper and Lower Bounds to the Eigenvalues of Double-Minimum Potentials
The Journal of Chemical Physics, 1965Several methods of obtaining upper and lower bounds to the eigenvalues of self-adjoint operators bounded from below have recently been developed by Löwdin. All these procedures are based on a bracketing theorem. We mention them and discuss one of the variants that makes use of intermediate Hamiltonians.
Carlos F. Bunge, Annik Vivier Bunge
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New inequalities for the minimum eigenvalue ofM-matrices
Linear and Multilinear Algebra, 2013Some new inequalities for the minimum eigenvalue of M-matrices are established. These inequalities improve the results in [G. Tian and T. Huang, Inequalities for the minimum eigenvalue of M-matrices, Electr. J. Linear Algebra 20 (2010), pp. 291–302].
Yaotang Li, Ruijuan Zhao, Chaoqian Li
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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, …,
Yuichi Yoshida, Suguru Tamaki
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On Maximizing the Minimum Eigenvalue of a Linear Combination of Symmetric Matrices
SIAM Journal on Matrix Analysis and Applications, 1989The problem considered is that of maximizing, with respect to the weights, the minimum eigenvalue of a weighted sum of symmetric matrices when the Euclidean norm of the vector of weights is constrained to be unity. A procedure is given for determining the sign of the maximum of the minimum eigenvalue and for approximating the optimal weights ...
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The eigenvalue problem for a double minimum potential
The Journal of Chemical Physics, 1975Frank L. Tobin, Juergen Hinze
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