Bounds for the singular values of a matrix involving its sparsity pattern.
Kolotilina, L.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
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Kolotilina, L.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
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Clive Elphick, Pawel Wocjan (2015)
Discussiones Mathematicae Graph Theory
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One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn. We recently generalised this bound to include all eigenvalues of the adjacency matrix. In this paper, we further generalize these results to include all eigenvalues of the adjacency, Laplacian and signless Laplacian matrices. The various known bounds...
Yang, Zhi Ming (2011)
Applied Mathematics E-Notes [electronic only]
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Shabnam Akhtari, Jeffrey D. Vaaler (2016)
Acta Arithmetica
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We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields. ...
J. Sun (1983)
Numerische Mathematik
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Manzini, Giovanni (1998)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Zhang, Juan, Liu, Jianzhou (2010)
Mathematical Problems in Engineering
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Guang-Da Hu, Qiao Zhu (2010)
Kybernetika
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This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.
Chen, Dong-Yan, Wang, De-Yu (2006)
Journal of Inequalities and Applications [electronic only]
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J. Kaczorowski, A. Perelli (2012)
Acta Arithmetica
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Ludwig F. Elsner, Christopher R. Johnson, M. Neumann (1982)
Czechoslovak Mathematical Journal
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