Controllability of matrix eigenvalue algorithms: the inverse power method |
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Authors: | U. Helmke P. A. Fuhrmann |
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Affiliation: | a Universität Würzburg, Institut für Mathematik, Würzburg, Germany;b Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel |
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Abstract: | 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 defined on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and sufficient condition for almost controllability of the inverse power method is derived. |
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Keywords: | Eigenvalue method Controllability Invariant subspaces Projective space |
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