Displaying similar documents to “Bounds of modulus of eigenvalues based on Stein equation”

New bounds for the minimum eigenvalue ofM-matrices

Feng Wang, Deshu Sun (2016)

Open Mathematics

Similarity:

Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.

Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

Jianxing Zhao, Caili Sang (2016)

Open Mathematics

Similarity:

Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.

Unified Spectral Bounds on the Chromatic Number

Clive Elphick, Pawel Wocjan (2015)

Discussiones Mathematicae Graph Theory

Similarity:

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...