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Controllability of matrix eigenvalue algorithms: the inverse power method

✍ Scribed by U. Helmke; P.A. Fuhrmann

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 140 KB
Volume: 41
Category: Article
ISSN: 0167-6911
DOI: 10.1016/s0167-6911(00)00039-6

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✦ Synopsis

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 deÿned on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and su cient condition for almost controllability of the inverse power method is derived.

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