  Although machine learning is increasingly applied in control approaches, only
few methods guarantee certifiable safety, which is necessary for real world
applications. These approaches typically rely on well-understood learning
algorithms, which allow formal theoretical analysis. Gaussian process
regression is a prominent example among those methods, which attracts growing
attention due to its strong Bayesian foundations. Even though many problems
regarding the analysis of Gaussian processes have a similar structure, specific
approaches are typically tailored for them individually, without strong focus
on computational efficiency. Thereby, the practical applicability and
performance of these approaches is limited. In order to overcome this issue, we
propose a novel framework called GP3, general purpose computation on graphics
processing units for Gaussian processes, which allows to solve many of the
existing problems efficiently. By employing interval analysis, local Lipschitz
constants are computed in order to extend properties verified on a grid to
continuous state spaces. Since the computation is completely parallelizable,
the computational benefits of GPU processing are exploited in combination with
multi-resolution sampling in order to allow high resolution analysis.
