Paper ID sheet UCL-INMA-2002.901

Title

A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

Authors

P.-A. Absil, R. Mahony, R. Sepulchre, P. Van Dooren

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 $A$. The cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.

Key words

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Status

SIAM Review, Vol. 44, No. 1, pp. 57-73 (2002). Related conference paper: Proceedings of the 39th IEEE Conference on Decision and Control (CDC 2000, Sydney).

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• Publisher's version: doi:10.1137/S0036144500378648
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Further information

Related links

• Conference paper (CDC 2000): PS file.
• 2002 SIAM Student Paper Prize presentation: PS file.
• SIAM Review.
• CDC 2000.
• SIAM 50th Anniversary and 2002 Annual Meeting.