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Restart Strategy.

The increasing storage or the computational overhead, for increasing dimension ${m}$ 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