Realization of the method of conjugate gradients on a graphic processor with application of matrix methods of SLAU solution

The paper presents an algorithm for solving SLAEs by the method of conjugate gradients on a graphics processor. A matrix container class based on NVIDIA CUDA technology is proposed as the main implementation tool. The performance of SLAE solution by Cramer and conjugate gradient methods was compared on the central and graphic processors. The results of the study have shown that the parallelized method of conjugate gradients performed on a graphics processor has the highest efficiency when processing SLAEs with a symmetric positively defined principal matrix. The considered approach for parallel processing of matrix operations has potential for application in various areas where large systems of equations need to be solved, such as in science, engineering and finance. Overall, this work is of practical relevance in the field of computational performance optimization and lays the foundation for solving many mathematical problems on a GPU.