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Restart Strategy.

The increasing storage or the computational overhead, for increasing
dimension of the subspace, may make it necessary to restart. An
obvious way to restart is to take the most recent approximation for the
desired eigenvector. However, this may not be the most efficient
strategy for restarting. With any restart by a single vector we discard
possibly valuable information that is contained in the remaining part of
the subspace. Unless we have an invariant subspace, all vectors in the
subspace contain information for the wanted eigenvector. After restart
with one single vector we see the effect of the lost information by a
slowdown in the speed of convergence. Therefore it is often better to
restart with a set of vectors representing a subspace that contains more
information for the wanted eigenpair, and a good strategy is to restart
with the subspace spanned by the Ritz vectors of a small number of the
Ritz values closest to a specified target value.

Susan Blackford
2000-11-20