  Closed-loop adaptive optics systems which use minimum mean square error
wavefront reconstruction require the computation of pseudo open loop wavefront
slopes. These techniques incorporate a knowledge of atmospheric statistics
which must therefore be represented within the wavefront slope measurements.
These pseudo open loop slopes are computed from the sum of the measured
residual slopes and the reconstructed slopes that would be given if the
deformable mirror was flat, generally involving the multiplication of an
interaction matrix with actuator demands from the previous time-step. When
using dense algebra, this multiplication is computationally expensive for
Extremely Large Telescopes, requiring a large memory bandwidth. Here we show
that this requirement can be significantly reduced, maintaining mathematical
correctness and significantly reducing system complexity. This therefore
reduces the cost of these systems and increases robustness and reliability.
