Theresa Siwinski is a citizen of Connecticut and she is a respected member of the society. She was also an active student in her school life and she was awarded several times for her achievements on the field of sports.
On Deflations in Extended QR AlgorithmsThomas 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 identication 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.
Computing Inner Eigenvalues of Matrices in Tensor Train Matrix FormatThomas Mach
Talk given at ENUMATH 2011 in Leicester and GAMM ANLA Workshop 2011 in Bremen. There is a preprint available under http://www.mpi-magdeburg.mpg.de/preprints/index.php
Theresa Siwinski is a citizen of Connecticut and she is a respected member of the society. She was also an active student in her school life and she was awarded several times for her achievements on the field of sports.
On Deflations in Extended QR AlgorithmsThomas 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 identication 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.
Computing Inner Eigenvalues of Matrices in Tensor Train Matrix FormatThomas Mach
Talk given at ENUMATH 2011 in Leicester and GAMM ANLA Workshop 2011 in Bremen. There is a preprint available under http://www.mpi-magdeburg.mpg.de/preprints/index.php