Circular trichotomy of the spectrum of regular matrix pencils
type: Item
instance of: scholarly article
title: Circular trichotomy of the spectrum of regular matrix pencils
zbMATH Open document ID: 1227.65034
author: Olivier Pourquier
author: M. Sadkane
author: A. Malyshev
published in: Linear Algebra and its Applications
publication date: 2011-06-08T00:00:00Z
review text: This paper presents a method for approximating right and left deflating subspaces of regular matrix pencils corresponding to eigenvalues in, on and out the complex unit circle. This work is an extension of a previous one, where the condition that there are no eigenvalues on the unit circle is relaxed here. The method consists in the construction of two matrix sequences whose null spaces and the null space of their sum lead to approximations of the deflating subspaces corresponding to eigenvalues moduli according to the unit circle, and then an orthogonalization is used to obtain the corresponding deflating subspaces. The convergence analysis is done and some examples shows the validity of the proposed method.
reviewed by: Edgar Pereira
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 65F25
zbMATH DE Number: 5905226
zbMATH Keywords: regular matrix pencil
zbMATH Keywords: Weierstrass canonical form
zbMATH Keywords: deflating subspace
zbMATH Keywords: numerical examples
zbMATH Keywords: eigenvalues
zbMATH Keywords: orthogonalization
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.laa.2010.06.019
OpenAlex ID: W2066179613
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DOI: 10.1016/J.LAA.2010.06.019
description: scientific article; zbMATH DE number 5905226