Paper ID sheet - Systems and Control Engineering at ULg
- TITLE: Cubically convergent iterations for invariant subspace
computation
- AUTHORS: P.-A. Absil, R. Sepulchre, P. Van Dooren, R. Mahony
- ABSTRACT:
We propose a Newton-like iteration that evolves on the set of fixed dimensional
subspaces of $\rr^n$ and converges locally cubically to the invariant subspaces
of a symmetric matrix. This iteration is compared in terms of numerical cost
and global behaviour with three other methods that display the same property
of cubic convergence. Moreover, we consider heuristics that greatly improve
the global behaviour of the iterations.
- STATUS: published in SIAM J. Matrix Analysis, vol. 26, 1, pp.
70-96, 2004.
- DATE OF ENTRY: January 2003.
- Published version: http://dx.doi.org/10.1137/S0895479803422002 [local copy].
- Preprint: PS file (with better quality figures).
- Shorter version focusing on Newton methods: ``A Newton algorithm
for invariant subspace computation with large basins of attraction'', P.-A.
Absil, R. Sepulchre, P. Van Dooren and R. Mahony, Proceedings of the 42nd
IEEE Conference on Decision and Control, December 9-12, 2003, Hyatt Regency
Maui, Hawaii, USA, pp. 2352-2357, December 2003.
BibTeX citation:
@article {AbsSepDooMah2004,
author = {P. A. Absil and R. Sepulchre and P. Van Dooren and R. Mahony},
title = {Cubically Convergent Iterations for Invariant Subspace Computation},
year = {2004},
journal = {SIAM J. Matrix Anal. Appl.},
fjournal = {SIAM Journal on Matrix Analysis and Applications},
volume = {26},
number = {1},
pages = {70--96},
keywords = {invariant subspace; Grassmann manifold; cubic convergence; symmetric eigenproblem; inverse iteration; Rayleigh quotient; Newton method; global convergence},
url = {http://link.aip.org/link/?SML/26/70/1},
doi = {10.1137/S0895479803422002}
issn = {0895-4798},
}
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