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By J.H. Jeans, M.A., F.R.S

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The matrix partition (U;l MUp can be written as (44) so that the columns of (U;f J( U; must simply be divided by the most recent eigenvalue estimates to yield (U;f MUp. The computation associated with this is negligible. Finally, given that Up = [Up- 1 U;_l <1>]Qp, the lower left partitions of k p and Mp can be written in terms of the lower rows of the previous reduced matrices k p - 1 and Mp _ 1 as (45) and (46) so that they can also be obtained with very little effort. It should be noted that subspace repetition requires that some previous results must be saved for the refinement procedure, and that some straightforward changes must be made to the refinement procedure.

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