Paper ID sheet UCL-INMA-2004.903


Cubically convergent iterations for invariant subspace computation

P.-A. Absil, R. Sepulchre, P. Van Dooren, R. Mahony
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.
Key words
published in SIAM J. Matrix Analysis, vol. 26, 1, pp. 70-96, 2004
BibTeX entry

@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 = {},
doi = {10.1137/S0895479803422002}
issn = {0895-4798},
Further information
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.