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A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces

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Date

2002

Authors

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

Journal Title

Journal ISSN

Volume Title

Publisher

SIAM Publications

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.

Description

Keywords

Keywords: Algorithms; Convergence of numerical methods; Eigenvalues and eigenfunctions; Invariance; Matrix algebra; Problem solving; Riccati equations; Grassmann manifold; Grassmann-Rayleigh quotient iteration; Invariant subspaces; Iterative methods Grassmann manifold; Invariant subspace; Rayleigh quotient iteration

Citation

URI

http://hdl.handle.net/1885/94417

Collections

ANU Research Publications

Source

SIAM Review

Type

Journal article

Book Title

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