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.
%0 Generic
%1 absil2002grassmann
%A Absil, P.A.
%A Mahony, R.
%A Sepulchre, R.
%A Dooren, P. Van
%B Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
%D 2002
%K eigenvalues grassman iteration power-method rayleigh stiefel-manifolds
%P 4241--4246
%R 10.1137/S0036144500378648
%T A Grassmann-Rayleigh quotient iteration for computing invariant subspaces
%V 5
%X 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.
%@ 0780366387
@conference{absil2002grassmann,
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.},
added-at = {2011-02-17T21:28:22.000+0100},
author = {Absil, P.A. and Mahony, R. and Sepulchre, R. and Dooren, P. Van},
biburl = {https://www.bibsonomy.org/bibtex/270f026197ffb8eee7a50b84be6e1a3cc/ytyoun},
booktitle = {Decision and Control, 2000. Proceedings of the 39th IEEE Conference on},
doi = {10.1137/S0036144500378648},
interhash = {6d23a8ff3fa3b2880b9ac085b9dfe6dd},
intrahash = {70f026197ffb8eee7a50b84be6e1a3cc},
isbn = {0780366387},
keywords = {eigenvalues grassman iteration power-method rayleigh stiefel-manifolds},
organization = {IEEE},
pages = {4241--4246},
timestamp = {2011-10-01T07:37:15.000+0200},
title = {{A Grassmann-Rayleigh quotient iteration for computing invariant subspaces}},
volume = 5,
year = 2002
}