  This paper introduces a parallel implementation in CUDA/C++ of the Gaussian
process with a decomposed kernel. This recent formulation, introduced by Joukov
and Kuli\'c (2022), is characterized by an approximated -- but much smaller --
matrix to be inverted compared to plain Gaussian process. However, it exhibits
a limitation when dealing with higher-dimensional samples which degrades
execution times. The solution presented in this paper relies on parallelizing
the computation of the predictive posterior statistics on a GPU using CUDA and
its libraries. The CPU code and GPU code are then benchmarked on different
CPU-GPU configurations to show the benefits of the parallel implementation on
GPU over the CPU.
