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

## 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 |
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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: | 04 Feb 2015 22:50 |

Last Modified: | 05 Feb 2015 08:22 |

DOI: |