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A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

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Absil, Pierre-Antoine [UCL] Mahony, R. Sepulchre, Rodolphe [UCL] Van Dooren, Paul [UCL]

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 RQl 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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2002
Language Anglais
Journal information "SIAM Review" - Vol. 44, no. 1, p. 57-73 (2002)
Peer reviewed yes
Publisher Siam Publications (Philadelphia)
issn 0036-1445
e-issn 1095-7200
Publication status Publié
Affiliation UCL - FSA/INMA - Département d'ingénierie mathématique
Keywords Rayleigh quotient iteration ; invariant subspace ; Grassmann manifold
Links
Bibliographic reference Absil, Pierre-Antoine ; Mahony, R. ; Sepulchre, Rodolphe ; Van Dooren, Paul. A Grassmann-Rayleigh quotient iteration for computing invariant subspaces. In: SIAM Review, Vol. 44, no. 1, p. 57-73 (2002)
Permanent URL http://hdl.handle.net/2078.1/42131