GAUSSIAN ELIMINATION ON HYPERCUBES.

We compare several implementations of the Gaussian elimination algorithm for solving dense linear systems on hypercube parallel processors. We distinguish between two classes of methods: methods that require to move the elimination row (or column) to all processors before the elimination proceeds, and methods that require only moving data to nearest neighbors. Algorithms of the second class, which we call pipelined algorithms, require only a ring or grid structure which is embedded into the hypercube. One of our main conclusions is that for Gaussian elimination the additional connectivity of the hypercube topology over that a two-dimensional grid of processors does not help much in improving efficiency. Another result of our analysis is that there is little reason for using row or column type algorithms instead of grid algorithms. One of the goals of the paper is also to show a simple model of complexity analysis at work, by comparing the estimated times that it provides with the actual execution times.