Dense Matrix techniques for the CRAY-1 and CRAY X-MP supercomputers.

This memorandum presents a tutorial on algorithms and programming examples for dense matrix operations on the CRAY-1 and CRAY X-MP supercomputers. The architectural differences between a CRAY-1 and a CRAY X-MP are highlighted, with emphasis of the impact of those differences on FORTRAN program performance. Then a review of dense matrix techniques that have been presented in the literature is made. Results using these dense matrix techniques for both the CRAY-1 and the CRAY X-MP are presented, with FORTRAN examples of these techniques for clarity. Detailed discussions of both matrix multiplication and LU factorization operations are presented. From these results, some general principles of matrix operation techniques on the CRAY X-MP can be drawn.