Figure 12

The pre-condition of the Outside VMT algorithm. (a) An illustration of the matrix A upon computing A_{I, J}(dotted entries). (b) An illustration of the pre-computed matrix β. The pre-condition requires that all entries in the sub-matrix A_{[0,I], [J,n]}, excluding A_{I, J}, are computed (dark and light gray entries). In addition, A_{I, J}is either the result of the matrix multiplication (β_[0,I),I)^T ⊗ α_{[0,I), J}(the multiplication of the transposed striped dark gray matrix in β with the striped dark gray matrix in A), or the multiplication α_{I,(J, n]}⊗ (β_{J,(J, n]})^T (the multiplication of the non-striped dark gray matrix in A with the transposed non-striped dark gray matrix in β).