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A Newton algorithm for invariant subspace computation with large basins of attraction

Absil, P-A; Sepulchre, R; Van Dooren, P; Mahony, Robert


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.

CollectionsANU Research Publications
Date published: 2003
Type: Conference paper
Source: Proceedings of the 42nd IEEE Conference on Decision and Control


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