A note on the inversion of Sylvester matrices in control systems
type: Item
instance of: scholarly article
title: A note on the inversion of Sylvester matrices in control systems
zbMATH Open document ID: 1217.65058
DOI: 10.1155/2011/609863
author: Hongkui Li
author: Ranran Li
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/225809
review text: Summary: We give a sufficient condition (the solvability of two standard equations) of a Sylvester matrix by using the displacement structure of the Sylvester matrix, and, according to the sufficient condition, we derive a new fast algorithm for the inversion of a Sylvester matrix, which can be denoted as a sum of products of two triangular Toeplitz matrices. The stability of the inversion formula for a Sylvester matrix is also considered. The Sylvester matrix is numerically forward stable if it is nonsingular and well conditioned.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 15B05
zbMATH DE Number: 5904905
zbMATH Keywords: Sylvester matrix
zbMATH Keywords: algorithm
zbMATH Keywords: inversion
zbMATH Keywords: triangular Toeplitz matrices
zbMATH Keywords: stability
Wikidata QID: Q58693293
MaRDI profile type: Publication
OpenAlex ID: W1993763611
cites work: Q3014260
cites work: Q3359644
cites work: The weak and strong stability of algorithms in numerical linear algebra
description: scientific article; zbMATH DE number 5904905