Figure 14

The horizontal decomposition in the Outside VMT algorithm, for the case where | I | > | J |. (a) A_{I, J}sustains the pre-condition (see Figure 12 for notations). (b) A_{I, J}is partitioned horizontally to $A_{I_1,J}$ and $A_{I_2,J}$, where $A_{I_1,J}$ is computed recursively. (c) If μ_{i, j}is of the form ⊕_q∈[0,i)(β_{q, i}⊗ α_{q, j}), then the pre-condition for computing $A_{I_2,J}$ is established, by updating $A_{I_2,J}$ to be $A_{I_2,J}\oplus \left({\left({\beta }_{L,I_2}\right)}^T\otimes A_{L,J}\right)$ (in this example L = I₁, since I₂ ends before J starts. The corresponding sub-matrix of β is not shown). In the case where μ_{i, j}= ⊕_q∈(j,n](α_{i, q}⊗ β_{j, q}), the pre-condition is met without any need for performing a matrix multiplication. Then, $A_{I_2,J}$ is computed recursively (not shown).