Seminars

Large sparse linear systems of the kind Ax = b must be solved in many applications in science and engineering. The most reliable solutions for these systems are the direct approaches, but they are expensive in terms of memory utilization and time-to-solution. Low-rank representations have recently been added to these solvers in this regard to decrease their time and memory requirements. In this work, our goal is to evaluate and improve the update process using low-rank matrices within the PaStiX solver. For this purpose, we introduced many approaches in order to seek the best one. We performed compression and accumulation in different steps. Then, we focused on making the best decision at each update. Firstly, we studied the cons and pros of each approach using theoretical and numerical results. Secondly, we defined a new strategy based on the results that we had. Finally, we implemented and compared the new method to the other methods. We illustrated also the strengths and limitations of this new technique.
Thanks to these approaches, we managed to find an efficient way to optimize memory usage and computational costs during the update of low-rank matrices.