Cubically Convergent Iterations for Invariant Subspace Computation

Authors:
P.-A. Absil;R. Sepulchre;P. Van Dooren;R. Mahony
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2005

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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 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.