GPU acceleration of splitting schemes applied to differential matrix equations
For researchers in optimal control and related fields, this work provides a practical method to accelerate numerical solutions of differential matrix equations, though it is an incremental application of existing techniques.
The paper investigates GPU acceleration of splitting schemes for differential Lyapunov and Riccati equations, achieving large speed-ups for sufficiently large matrices in numerical experiments.
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their solution, one may use several different kinds of numerical methods. Of these, splitting schemes are often a very competitive choice. In this article, we investigate the use of graphical processing units (GPUs) to parallelize such schemes and thereby further increase their effectiveness. According to our numerical experiments, large speed-ups are often observed for sufficiently large matrices. We also provide a comparison between different splitting strategies, demonstrating that splitting the equations into a moderate number of subproblems is generally optimal.