A Grassmann--Rayleigh Quotient Iteration for Computing Invariant Subspaces

Authors:
P.-A. Absil;R. Mahony;R. Sepulchre;P. Van Dooren
Affiliations:
-;-;-;-
Venue:
SIAM Review
Year:
2002

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Abstract

The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.