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Suppose that the generalized Schur form (8.12) is
ordered with respect to
such that
where
is the dimension of
. Then, for
, the
space
spanned by the first
columns
of
contains the
most promising Petrov vectors.
The corresponding test subspace is given by
.
Therefore, in order to reduce the dimension of the subspaces (``implicit
restart'') to
,
, the columns
through
and
through
can simply be discarded
and the Jacobi-Davidson algorithm can be continued with
Susan Blackford
2000-11-20