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Hauka laada maskott
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De ation procedures are one of the core parts of every iterative eigenvalue al- gorithm. In this lecture we discuss the de ation criterion used in the extended QR algorithm based on the chasing of rotations. We show that this de ation 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 de ation to the new extended QR algorithms. Aggressive early de ation is the key technique for the identi cation and de ation of already converged eigenvalues. Often these possibilities for de ation are not detected by the standard technique. We present numerical results underpinning the power of aggressive early de ation in the context of extended QR algorithms. These ideas can be further generalized to middle de ations in the setting of extended QR algorithms.
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This talk is a shorted version of the talk given in Aachen.
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Theresa siwinski
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theresasiwinski
Presentation of the paper http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW654.abs.html at the SLA 2014 in Kalamat, Greece
Fast and backward stable computation of roots of polynomials
Fast and backward stable computation of roots of polynomials
Thomas Mach
De ation procedures are one of the core parts of every iterative eigenvalue al- gorithm. In this lecture we discuss the de ation criterion used in the extended QR algorithm based on the chasing of rotations. We show that this de ation 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 de ation to the new extended QR algorithms. Aggressive early de ation is the key technique for the identi cation and de ation of already converged eigenvalues. Often these possibilities for de ation are not detected by the standard technique. We present numerical results underpinning the power of aggressive early de ation in the context of extended QR algorithms. These ideas can be further generalized to middle de ations in the setting of extended QR algorithms.
On Deflations in Extended QR Algorithms
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Maskott
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Kristi ja Anne
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