ylfink@water.waterloo.edu (ylfink) (11/16/88)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
SCIENTIFIC COMPUTATION SEMINAR
- Thursday, November 24, 1988
Dr. Angelika Bunse-Gerstner, Universitat Bielefeld,
West Germany, will speak on ``Symplectic Eigenvalue
Algorithms''.
TIME: 4:00 PM
ROOM: DC 1304
ABSTRACT
In several areas of application matrix eigenvalue
problems Mx = lambda x arise, in which the matrix M has a
special symmetry structure. It can be described by
symmetries of JM, where
J = [ 0 I]
-I 0
and I is the identity. The symmetry structure implies
that the eigenvalues of M occur pairwise and for some
of these problems the eigenvalue pairs have to be
separated. The usual eigenvalue algorithms for the
computation of the Schur form cannot exploit these
structures. They treat the eigenvalue problem like an
unstructured one. In particular because of rounding
errors they may lose the pairing for the computed
eigenvalues. For some of these problems eigenvalue
algorithms based on symplectic similarity
transformations can be developed, which preserve the
symmetry structure throughout the process. They need
only half the work and storage of the conventional
algorithms to compute a matrix R of a modified Schur
form. The eigenvalue pairing is preserved, more
precisely the computed R is exactly similar to M+E,
where E is a matrix with small norm having the same
structure as M. In this talk examples of problems are
given which lead to such eigenvalue computations and it
is shown how symplectic eigenvalue algorithms can be
- 2 -
developed for these problems.
November 16, 1988