The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Matrix bounds for the solution of the continuous algebraic Riccati equation.”

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...

Heights, regulators and Schinzel's determinant inequality

Shabnam Akhtari, Jeffrey D. Vaaler (2016)

Acta Arithmetica

Similarity:

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. ...

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.

Bounds of modulus of eigenvalues based on Stein equation

Guang-Da Hu, Qiao Zhu (2010)

Kybernetika

Similarity:

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.