GPU acceleration of splitting schemes applied to differential matrix equations

TL;DR

This paper explores the use of GPU acceleration to enhance the efficiency of splitting schemes for solving differential Lyapunov and Riccati equations, which are vital in optimal control, demonstrating significant speed-ups for large matrices.

Contribution

It introduces GPU-based parallelization of splitting schemes for differential matrix equations and compares different splitting strategies to identify optimal approaches.

Findings

Significant speed-ups observed with GPU acceleration for large matrices.

Splitting into a moderate number of subproblems is generally optimal.

GPU parallelization enhances the practicality of solving large-scale differential equations.

Abstract

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.