  We present a class of fast subspace tracking algorithms based on orthogonal
iterations for structured matrices/pencils that can be represented as small
rank perturbations of unitary matrices. The algorithms rely upon an updated
data sparse factorization -- named LFR factorization -- using orthogonal
Hessenberg matrices. These new subspace trackers reach a complexity of only
$O(nk^2)$ operations per time update, where $n$ and $k$ are the size of the
matrix and of the small rank perturbation, respectively.
