CUED Publications database

Cubically convergent iterations for invariant subspace computation

Absil, P-A and Sepulchre, R and Van Dooren, P and Mahony, R (2005) Cubically convergent iterations for invariant subspace computation. SIAM Journal on Matrix Analysis and Applications, 26. pp. 70-96. ISSN 0895-4798

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Abstract

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

Item Type: Article
Uncontrolled Keywords: Cubic convergence Global convergence Grassmann manifold Invariant subspace Inverse iteration Newton method Rayleigh quotient Symmetric eigenproblem
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:28
Last Modified: 08 Dec 2014 02:25
DOI: 10.1137/S0895479803422002