Optimality for Parallel Point-wise and Block-wise Resolution of a Triangular System on Homogeneous Environments

We consider both point-wise and block-wise versions for solving a linear triangular system on homogeneous machines. With p identical processors and for a problem of size N where N/r=n=2pq+1 (q≥3 and r being the block-size), we design an optimal parallel algorithm. We show its optimality in terms of both computing and communication costs. Finally, we determine the optimal value of the block size which minimizes the parallel execution time. A series of experimentations confirm the theoretical results.