High-performance Processing of Covariance Matrices Using GPU Computations

Practical applicability of many statistical algorithms is limited by large sizes of corresponding covariance matrices. These limitations can be significantly weakened due to effective use of the structure of covariance matrices, properties of the autocorrelation function, and advantages of the architecture of modern GPUs. This paper presents GPU implementations of the algorithms for inversion of a covariance matrix and solution of a system of linear equations whose coefficient matrix is a covariance matrix. Inversion of close to sparse covariance matrices is also considered in the work. For all the cases considered, significant accelerations were obtained in comparison with Octave mathematical software and ViennaCL computational library. For example, implemented algorithm of solution of a linear system was 6 times faster as compared with the implementation of Octave on the CPU and 3 times faster as compared with the ViennaCL implementation on the GPU for general matrices. The performance of inversion of a covariance matrix was 14 times faster than inversion algorithm of Octave on the CPU and 6 times faster than ViennaCL inversion algorithm on GPU.