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.
• STATUS:
  • Full paper: SIAM Review, Vol. 44, No. 1, pp. 57-73 (2002).
  • Conference paper: Proceedings of the 39th IEEE Conference on Decision and Control (CDC 2000, Sydney).
• DATE OF ENTRY: March 2001.

• Published version: http://dx.doi.org/10.1137/S0036144500378648 [ps,pdf].
• 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.