Controllability of matrix eigenvalue algorithms: the inverse power method

Authors
Helmke, U Fuhrmann, PA
Citation
U. Helmke et Pa. Fuhrmann, Controllability of matrix eigenvalue algorithms: the inverse power method, SYST CONTR, 41(1), 2000, pp. 57-66
Citations number
7
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
SYSTEMS & CONTROL LETTERS
ISSN journal
01676911 → ACNP
Volume
41
Issue
1
Year of publication
2000
Pages
57 - 66
Database
ISI
SICI code
0167-6911(20000915)41:1<57:COMEAT>2.0.ZU;2-X
Abstract
In this paper we initiate a program to study the controllability properties of matrix eigenvalue algorithms arising in numerical linear algebra. Our f ocus is on a well-known eigenvalue method, the inverse power iteration defi ned on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a nec essary and sufficient condition for almost controllability of the inverse p ower method is derived. (C) 2000 Elsevier Science B.V. All rights reserved.