Note on structured indefinite perturbations to Hermitian matrices
type: Item
instance of: scholarly article
title: Note on structured indefinite perturbations to Hermitian matrices
zbMATH Open document ID: 1124.15005
author: Kui Du
published in: Journal of Computational and Applied Mathematics
publication date: 2007-04-13T00:00:00Z
review text: Results of \textit{M. L. Overton} and \textit{P. van Dooren} [On computing the complex passivity radius. Proc. IEEE Conference on decision Control (to appear)] about certain structured perturbations of Hermitian matrices are generalised to the case of skew-Hermitian, Hamiltonian and skew-Hamiltonian matrices. The questions considered are the following: Is there a structured perturbation such that the perturbed matrix is singular? What is the smallest (in operator norm) such perturbation? These questions are answered for the abovementioned classes and for two classes of perturbations, additive ones and multiplicative ones. In the skew-Hamiltonian case also the distance to a matrix with a real eigenvalue is given. A numerical method to calculate these distances is sketched and an example is given.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 5142295
zbMATH Keywords: structured additive perturbations
zbMATH Keywords: structured multiplicative perturbations
zbMATH Keywords: skew-Hermitian matrix
zbMATH Keywords: Hamiltonian matrix
zbMATH Keywords: skew-Hamiltonian matrix
zbMATH Keywords: eigenvalue
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
full work available at URL: j.cam.2006.02.030
OpenAlex ID: W2012697994
cites work: On Stable Eigendecompositions of Matrices
cites work: A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices
cites work: A fast algorithm for the computation of an upper bound on the \(\mu\)-norm
cites work: A formula for computation of the real stability radius
cites work: Q4895203
cites work: Structured pseudospectra for polynomial eigenvalue problems, with applications
DOI: 10.1016/J.CAM.2006.02.030
description: scientific article; zbMATH DE number 5142295