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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE015465442
Author(s):
Ipsen, Ilse C. F.:
Shorttitle:
Overview of relative sin theta theorems for invariant subspaces
Source:
J. Comput. Appl. Math. 123, No. 1-2, 131-153 (2000).
Classification:
Primary Classification:
65F15Eigenvalues, eigenvectors
Secondary Classification:
15A45Miscellaneous inequalities involving matrices
15A42Inequalities involving eigenvalues and eigenvectors
65F35Matrix norms, conditioning, scaling
Keywords:
invariant subspace, rotation by perturbation, bounds on angle, dependence on eigenvalues, grading and scaling, reliable computation of eigenvectors
Review:

A complex square matrix is assumed to possess an invariant
subspace, and a change of this subspace under a perturbation is
measured by a certain ``pricipal" angle. For its sinus, a number
of estimates is reviewed/listed for both the additive and
multiplicative perturbations and different assumptions about the
matrix. The review, a successor of similar surveys, offers another
set of explanations why certain high-accuracy diagonalization
methods are so reliable. It is well written and well
understandable, with both the ideas and technicalities amply
illustrated by the three-dimensional or partitioned examples.
Remarks to the editors: