Energy-aware solution of linear systems with many right hand sides
Martin Köhler, Carolin Penke, Jens Saak, Pablo Ezzatti · Computer Science - Research and Development · 2016
The solution of linear systems of equations with many right hand sides is mostly seen as a trivial extension of solving a linear system and the algorithmic developments mostly focus on the efficient computation of the LU decomposition. This is, however, not regarding the case where many right hand sides increase the runtime influence of the forward/backward substitution. In this contribution we present a GPU accelerated Gauss–Jordan-elimination based all-at-once solution scheme which focuses on minimizing the runtime and the energy consumption by switching the forward/backward substitution in favor of a more suitable operation. We obtain a multi-GPU aware algorithm which is up to 2.5 times faster than the current state-of-the-art LU decomposition based solution process of MAGMA and saves 48 % required energy.