Application of the CUDA architecture for implementation of grid-based algorithms for the method of moving separation of mixtures

The paper presents the implementation of the grid methods for finding maximum likelihood estimators in the mixed probability models based on the software solutions for the computations on GPUs using the NVIDIA CUDA technology. The hierarchy of programming classes is described, an approach to the initial estimation and further modification of the parametric grids is proposed, and the convergence speed and other characteristics of the developed methods are examined by the test data sets. The key characteristics of the method including the change of approximation error by the $l^1$ metric and reducing the number of components under the iterative steps are demonstrated by the graphs. The integration of the implemented software modules with the specialized online service for real data processing MSM Tools is also discussed.