Iterative methods for fixed point problems on high performance computing environment

It takes considerable effort to develop cost-effective, efficient parallel algorithms in a high performance computing environment for computationally intensive problems arising from many areas, such as complex systems dynamics and molecular sequence analysis. In this work, we demonstrate some steps which guide us to design an efficient parallel algorithm. An ill-conditioned problem, which is the case for most complex systems, is selected to identify the appropriate parameters for a successive over relaxation (SOR) algorithm. It is illustrated that once the right parameters are identified, they also help to select an appropriate type of parallel algorithm to be developed for a particular problem.