Дослідження паралельних алгоритмів розв’язання заповнених систем лінійних рівнянь

Abstract

Methods for solving densely populated linear systems of equations using parallel computing have been developed. The effectiveness of parallelization of classical iterative methods, such as the Jacobi method, the Gauss-Seidel method, and the upper relaxation method, has been analyzed. The influence of the distribution of the computational load between processors on the speed of algorithms has been studied, taking into account the features of multi-core and cluster architectures. Experimental results for various configurations of multi-core processors and cluster systems have been presented. Optimal parallelization strategies for increasing computing performance have been determined. The possibilities of using modern parallel programming libraries OpenMP and MPI for implementing effective algorithms for solving large systems of equations have been considered.