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The main advantages of a numerically stable deflation strategy are the reduction of the working size of the reduction and the ability to determine clusters of nearby eigenvalues without requiring the block size to be greater than or equal to the size of the cluster. The deflation scheme developed for the BIRAM implementation is an extension of the techniques discussed in §7.6. We refer the reader to this section for further details.

An algorithmic issue that arises is how to handle situations where the number of converged vectors to be locked is not a multiple of the block size. At the completion of the deflation procedure, the active reduction has an incomplete last block. To simplify the implicit restarting mechanism, we fill out this last block so that the active reduction is of length $m \cdot b.$

Susan Blackford 2000-11-20