A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

P. A. Absil; R. Mahony; R. Sepulchre; P. Van Dooren

doi:10.1137/S0036144500378648

A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

P. A. Absil^*, R. Mahony, R. Sepulchre, P. Van Dooren

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

54 Citations (Scopus)

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.

Original language	English
Pages (from-to)	57-73
Number of pages	17
Journal	SIAM Review
Volume	44
Issue number	1
DOIs	https://doi.org/10.1137/S0036144500378648
Publication status	Published - Mar 2002
Externally published	Yes

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title = "A Grassmann-Rayleigh quotient iteration for computing invariant subspaces",

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.",

keywords = "Grassmann manifold, Invariant subspace, Rayleigh quotient iteration",

author = "Absil, {P. A.} and R. Mahony and R. Sepulchre and {Van Dooren}, P.",

year = "2002",

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AU - Mahony, R.

AU - Sepulchre, R.

AU - Van Dooren, P.

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N2 - 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.

AB - 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.

KW - Grassmann manifold

KW - Invariant subspace

KW - Rayleigh quotient iteration

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U2 - 10.1137/S0036144500378648

DO - 10.1137/S0036144500378648

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VL - 44

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JO - SIAM Review

JF - SIAM Review

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A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

Abstract

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