A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces
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
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Source
SIAM Review
Type
Journal article