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

Craig C. Douglas
IBM T. J. Watson Research Center
Yorktown Heights, NY, USA and
Computer Science Department
Yale University
New Haven, CT, USA


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.

Contributed November 30, 1992.