5.4.2 Data flow of the Gauß-Seidel forward iteration

As presented in Alg. 5.7 and Fig. 5.2 the components of  $\underline{u}^k$ are coupled, e.g., $u_i^k$ cannot be calculated before $u_{i-1}^k$ was determined. In general, all $u_{s}^k$ ($s<i$) for which $K_{i,s}\neq 0$ (graph/pattern of matrix) holds have to be calculated before $u_i^k$ can be updated.

Figure 5.2: Data flow of Gauß-Seidel forward iteration

Due to that coupling of the components of $\underline{u}^k$ the direct parallelization will become fine grain and the vectorization makes no sense.