Uwe Helmke, Fabian Wirth
On controllability of the real shifted inverse power iteration.
Preprint series: Report 453, Institut für Dynamische Systeme, Universität Bremen
65F15 Eigenvalues, eigenvectors
93B05 Controllability
We study the inverse power method well-known in numerical linear
algebra from a control point of view. In particular, controllability
properties of the inverse power method on projective space are
investigated. It is known that for complex eigenvalue shifts a simple
characterization of the reachable sets in terms of invariant subspaces
can be obtained. In contrast, the real case under consideration in
this talk is more complicated. Using properties of universally
regular controls, 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, controllability, projective space, universal controls