Some remarks on completely vectorizing point Gauss-Seidel while using the natural ordering

A common statement in papers in the vectorization field is to note that point SOR methods with the natural ordering cannot be vectorized. The usual approach is to reorder the unknowns using a red-black or diagonal ordering and vectorize that. In this paper we construct a point Gauss-Seidel iteration which completely vectorizes and still uses the natural ordering. The work here also applies to both point SOR and single program, multiple data (SPMD) parallel computer architectures. When this approach is reasonable to use is also shown. © 1994 J.C. Baltzer AG, Science Publishers.