A modified low-rank Smith method for large-scale Lyapunov equations
type: Item
instance of: scholarly article
title: A modified low-rank Smith method for large-scale Lyapunov equations
zbMATH Open document ID: 1034.93020
DOI: 10.1023/A:1022205420182
author: Danny C. Sorensen
author: Serkan Gugercin
author: A. C. Antoulas
published in: Numerical Algorithms
publication date: 2003-05-11T00:00:00Z
review text: The authors present a modified cyclic low-rank Smith method to compute low-rank approximations to solutions of Lyapunov equations arising from large-scale dynamical systems. Unlike the original cyclic low-rank Smith method introduced by \textit{T. Penzl} [SIAM J. Sci. Comput. 21, 1401--1418 (2000; Zbl 0958.65052)], the number of columns required by the modified method in the approximate solution does not necessarily increase at each step and is usually much lower than in the original cyclic low-rank Smith method. The modified method never requires more columns than the original one. Upper bounds are established for the errors of the low-rank approximate solutions and also for the errors in the resulting approximate Hankel singular values. Numerical results are given to verify the efficiency and accuracy of the new algorithm.
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93A15
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93B11
zbMATH DE Number: 1908559
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: Smith method
zbMATH Keywords: ADI iteration
zbMATH Keywords: model reduction
zbMATH Keywords: large-scale dynamical systems
zbMATH Keywords: approximate solutions
zbMATH Keywords: approximate Hankel singular values
reviewed by: A. A. Martynyuk
MaRDI profile type: Publication
full work available at URL: a:1022205420182
OpenAlex ID: W1586178554
description: scientific article; zbMATH DE number 1908559