Дослідження паралельних методів розв’язання систем нелінійних рівнянь

Abstract

Parallel methods for solving systems of nonlinear equations are considered, their basic concepts and efficiency in comparison with sequential algorithms. Mathematical models and algorithms used for parallelizing calculations are analyzed. Particular attention is paid to the implementation of Newton's methods, relaxation and iterative approaches in parallel computing environments. The impact of parallel computing on the speed and scalability of algorithms is studied, taking into account the use of multi-threaded and multi-processor architectures. The performance and scalability of the selected methods are analyzed, and the possibilities of their optimization are investigated.