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Displaying 41 – 55 of 55

Bounds of modulus of eigenvalues based on Stein equation

Guang-Da Hu, Qiao Zhu (2010)

Kybernetika

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.

Bounds of the matrix eigenvalues and its exponential by Lyapunov equation

Guang-Da Hu, Taketomo Mitsui (2012)

Kybernetika

We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix. Based on the relations between the real parts of the eigenvalues and the weighted logarithmic matrix norms, we derive both lower and upper bounds of the matrix exponential, which complement and improve the existing results in the literature. Some numerical examples are also...

Bounds on Laplacian eigenvalues related to total and signed domination of graphs

Wei Shi, Liying Kang, Suichao Wu (2010)

Czechoslovak Mathematical Journal

A total dominating set in a graph $G$ is a subset $X$ of $V (G)$ such that each vertex of $V (G)$ is adjacent to at least one vertex of $X$ . The total domination number of $G$ is the minimum cardinality of a total dominating set. A function $f : V (G) \to {- 1, 1}$ is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of an SDF is the sum of its function values over all vertices. The signed domination number of $G$ is the minimum weight of an SDF on $G$ . In this paper...

Bounds on the coefficients of the characteristic and minimal polynomials.

Dumas, Jean-Guillaume (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices.

Horn, Roger A., Zhang, Fuzhen (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Bounds on the spectral radius of Hadamard products of positive operators on $l_{p}$ -spaces.

Schep, Anton R. (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Bounds on the subdominant eigenvalue involving group inverses with applications to graphs

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

Let $A$ be an $n \times n$ symmetric, irreducible, and nonnegative matrix whose eigenvalues are $λ_{1} > λ_{2} \geq ... \geq λ_{n}$ . In this paper we derive several lower and upper bounds, in particular on $λ_{2}$ and $λ_{n}$ , but also, indirectly, on $μ = {max}_{2 \leq i \leq n} | λ_{i} |$ . The bounds are in terms of the diagonal entries of the group generalized inverse, $Q^{#}$ , of the singular and irreducible M-matrix $Q = λ_{1} I - A$ . Our starting point is a spectral resolution for $Q^{#}$ . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected...

Brascamp--Lieb inequalities for non-commutative integration.

Carlen, Eric A., Lieb, Elliott H. (2008)

Documenta Mathematica