Proper deflating subspaces: Properties, algorithms and applications
type: Item
instance of: scholarly article
title: Proper deflating subspaces: Properties, algorithms and applications
zbMATH Open document ID: 0804.65047
DOI: 10.1007/BF02140690
published in: Numerical Algorithms
publication date: 1995-01-22T00:00:00Z
review text: Let \(\lambda M - N\) with \(M,N \in \mathbb{R}^{p \times q}\) be an arbitrary matrix pencil. The space \({\mathcal V}\), spanned by the columns \(V \in \mathbb{R}^{q \times r}\) is called a proper \(C_ 1\) deflating subspace if for some \(S \in \mathbb{R}^{r \times r}\), \(NV = MVS\) with \(MV\) of full column rank and the eigenvalues of \(S\) in \(C_ 1\). This paper describes an algorithm to compute such (maximal) deflating subspaces. It refines existing algorithms by an efficient combination of an algorithm for computing the generalized Schur form of the pencil and an algorithm for pole placement of linear systems given in descriptor form. The algorithm can also be used to compute a stabilizing solution of a generalized or constrained Riccati equation for continuous as well as discrete time. The latter application is also discussed in some detail.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 640749
zbMATH Keywords: reducing subspace
zbMATH Keywords: matrix pencil
zbMATH Keywords: deflating subspace
zbMATH Keywords: algorithm
zbMATH Keywords: generalized Schur form
zbMATH Keywords: pole placement
zbMATH Keywords: Riccati equation
author: Cristian Oară
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02140690
OpenAlex ID: W2000661060
description: scientific article; zbMATH DE number 640749