Title: On Deflations in Extended QR Algorithms
Authors: Mach, Thomas ×
Vandebril, Raf #
Issue Date: 9-Sep-2013
Conference: GAMM Workshop Applied and Numerical Linear Algebra edition:2013 location:Wuppertal, Germany date:08-09 September 2013
Abstract: De deflation procedures are one of the core parts of every iterative eigenvalue algorithm. In this lecture we discuss the deflation criterion used in the extended QR algorithm based on the chasing of rotations. We show that this deflation criterion can be considered to be optimal with respect to absolute and relative perturbation of the eigenvalues.

Further, we present a generalization of aggressive early deflation to the new extended QR algorithms. Aggressive early deflation is the key technique for the identification and deflation of already converged eigenvalues. Often these possibilities for deflation are not detected by the standard technique. We present numerical results underpinning the power of aggressive early deflation in the context of extended QR algorithms. These ideas can be further generalized to middle deflations in the setting of extended QR algorithms.
Publication status: published
KU Leuven publication type: IMa
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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