Title: A generalization of the multishift QR-algorithm
Authors: Vandebril, Raf ×
Watkins, David S. #
Issue Date: 2012
Publisher: Society for Industrial and Applied Mathematics
Series Title: SIAM Journal on Matrix Analysis and Applications vol:33 issue:3 pages:759-779
Abstract: Recently a generalization of Francis’s implicitly shifted QR-algorithm was proposed, notably widening the class of matrices admitting low-cost implicit QR-steps. This unifying framework covered the methods and theory for Hessenberg and inverse Hessenberg matrices and furnished also new, single-shifted, QR-type methods for, e.g., CMV -matrices. Convergence of this approach was only suggested by numerical experiments. No theoretical claims supporting the results were presented. In this paper we present multishift variants of these new algorithms. We also provide a convergence theory that shows that the new algorithm performs nested subspace iterations on rational Krylov subspaces. Numerical experiments confirm the validity of the theory.
ISSN: 0895-4798
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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