Some Remarks on Completely Vectorizing Point Gauss-Seidel
                       While Using the Natural Ordering

                               Craig C. Douglas

                        Department of Computer Science
                               Yale University
                                P. O. Box 2158
                           New Haven, CT 06520-2158

                      E-mail: douglas-craig@cs.yale.edu


Abstract:  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 re-order 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 point SOR.  When this approach is reasonable to
use is also shown.