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

P. A. Absil; R. Sepulchre; P. Van Dooren; R. Mahony

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

P. A. Absil^*, R. Sepulchre, P. Van Dooren, R. Mahony

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	2352-2357
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	3
Publication status	Published - 2003
Event	42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: 9 Dec 2003 → 12 Dec 2003

Cite this

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title = "A Newton algorithm for invariant subspace computation with large basins of attraction",

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.",

keywords = "Cubic convergence, Global convergence, Grassmann manifold, Invariant subspace, Newton method, Symmetric eigenproblem",

author = "Absil, {P. A.} and R. Sepulchre and {Van Dooren}, P. and R. Mahony",

year = "2003",

language = "English",

volume = "3",

pages = "2352--2357",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "42nd IEEE Conference on Decision and Control ; Conference date: 09-12-2003 Through 12-12-2003",

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TY - JOUR

T1 - A Newton algorithm for invariant subspace computation with large basins of attraction

AU - Absil, P. A.

AU - Sepulchre, R.

AU - Van Dooren, P.

AU - Mahony, R.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - Cubic convergence

KW - Global convergence

KW - Grassmann manifold

KW - Invariant subspace

KW - Newton method

KW - Symmetric eigenproblem

UR - http://www.scopus.com/inward/record.url?scp=1542349067&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:1542349067

SN - 0743-1546

VL - 3

SP - 2352

EP - 2357

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - 42nd IEEE Conference on Decision and Control

Y2 - 9 December 2003 through 12 December 2003

ER -

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

Abstract

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