Controllabilityofmatrixeigenvaluealgorithms:theinverse powermethod (
Uwe Helmke · 2000
In this paper we initiate a program to study the controllability properties of matrix eigenvalue algorithms arising in numerical linear algebra. Our focus is on a well-known eigenvalue method, the inverse power iteration dened on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and sucient condition for almost controllability of the inverse power method is derived. c 2000 Elsevier Science B.V. All rights reserved.