Uwe Helmke, Fabian Wirth
Controllability of the shifted inverse power iteration: The case of real shifts
Preprint series: Proceedings Equadiff 99, Berlin, Germany, 1999
65F15 Eigenvalues, eigenvectors
93B05 Controllability
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 the solvability of this matrix
equation are given.

Keywords: inverse iteration, controllability, projective space, universal controls