clarke@csri.toronto.edu (Jim Clarke) (11/23/88)
NUMERICAL ANALYSIS SEMINAR - Friday, November 25, 10 a.m. in Room RS 310
(RS = Rosebrugh Building, 8 Taddle Creek Road)
Angelika Bunse-Gerstner
Universitat Bielefeld, West Germany
"Symplectic Eigenvalue Algorithms"
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 simi-
larity transformations can be developed, which preserve the symmetry struc-
ture 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
developed for these problems.
--
Jim Clarke -- Dept. of Computer Science, Univ. of Toronto, Canada M5S 1A4
(416) 978-4058
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