CUED Publications database

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

Absil, P-A and Sepulchre, R and Van Dooren, P and Mahony, R (2003) A Newton algorithm for invariant subspace computation with large basins of attraction. Proceedings of the IEEE Conference on Decision and Control, 3. pp. 2352-2357. ISSN 0191-2216

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: Cubic convergence Global convergence Grassmann manifold Invariant subspace Newton method Symmetric eigenproblem
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:46
Last Modified: 08 Dec 2014 02:25
DOI: