Lyapunov, Lanczos, and inertia

Authors
Antoulas, AC Sorensen, DC
Citation
Ac. Antoulas et Dc. Sorensen, Lyapunov, Lanczos, and inertia, LIN ALG APP, 326(1-3), 2001, pp. 137-150
Citations number
19
Categorie Soggetti
Mathematics
Journal title
LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN journal
00243795 → ACNP
Volume
326
Issue
1-3
Year of publication
2001
Pages
137 - 150
Database
ISI
SICI code
0024-3795(20010315)326:1-3<137:LLAI>2.0.ZU;2-W
Abstract
We present a new proof of the inertia result associated with Lyapunov equat ions. Furthermore, we present a connection between the Lyapunov equation an d the Lanczos process which is closely related to the Schwarz form of a mat rix. We provide a method for reducing a general matrix to Schwarz form in a finite number of steps (O(n(3))). Hence, we provide a finite method for co mputing inertia without computing eigenvalues. This scheme is unstable nume rically and hence is primarily of theoretical interest. (C) 2001 Elsevier S cience Inc. All rights reserved.