Figure 8

An exemplification of the vertical partition of B_{I, J}(the entries of B_{I, J}are dotted). (a) The pre-condition requires that all values in B_{[I,J], [I,J]}, excluding B_{I, J}, are computed, and B _{I, J} = β_I,(I,J)⊗ β _(I,J),J(see Figure 7). (b) B _{I, J} is partitioned vertically to $B_{I,J_1}$ and $B_{I,J_2}$, where $B_{I,J_1}$ is computed recursively. (c) The pre-condition for computing $B_{I,J_2}$ is established, by updating $B_{I,J_2}$ to be $B_{I,J_2}\oplus \left(B_{I,L}\otimes B_{L,J_2}\right)$ (in this example L = J₁, since I ends before J₁ starts). Then, $B_{I,J_2}$ is computed recursively (not shown).