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On controllability of the real shifted inverse power iteration |
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| Authors: | Uwe Helmke Fabian Wirth |
| Affiliation: | a Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany;b Zentrum für Technomathematik, Universität Bremen, D-28344 Bremen, Germany |
| Abstract: | Controllability properties of the inverse power method on projective space are investigated. For complex eigenvalue shifts a simple characterization of the reachable sets in terms of invariant subspaces can be obtained. The real case is more complicated and is investigated in this paper. Necessary and sufficient conditions for complete controllability are obtained in terms of the solvability of a matrix equation. Partial results on conditions for the solvability of this matrix equation are given. |
| Keywords: | Inverse iteration Forward accessibility Controllability Polynomial matrix equations |
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