Figure 2: A single pass of two-cyclic CSI-MSVD.
Figure 2 shows the dependencies involved in the steps of the above outlined procedure. The pipelined nature of the computation indicates that Steps 1, 2, and 3 described could be carried out concurrently. For example, the computation of the anti-diagonal elements (shown in the box labeled PHI in Figure 2) could be overlapped with the computation of the iterates and . Also, when the bidiagonal matrix has been updated with the elements and (the box labeled GAMMA) by using Equation (25), the approximation of eigenvalues through the bidiagonal-QR iteration could be done in parallel with the computation of the next anti-diagonal elements (, k+l=8 or k+l=10). Thus, the three functional components MATVEC, PHI, and GAMMA could be executed on three different processors. Information about the two-cyclic matrix M of Equation (2) is required only for the computations in MATVEC, so that the implementations of PHI and GAMMA is independent of the format used for storing the matrix.