A Newton algorithm for invariant subspace computation with large basins of attraction
We study the global behaviour of a Newton algorithm on the Grassmann manifold for invariant subspace computation. It is shown that the basins of attraction of the invariant subspaces may collapse in case of small eigenvalue gaps. A Levenberg-Marquardt-like modification of the algorithm with low numerical cost is proposed. A simple strategy for choosing the parameter is shown to dramatically enlarge the basins of attraction of the invariant subspaces while preserving the fast local convergence.
|Collections||ANU Research Publications|
|Source:||Proceedings of the 42nd IEEE Conference on Decision and Control|