Application of data-level parallelism to improve the efficiency of numerical methods

Purpose. The research is dedicated to examining the potential of data-level parallelism technology for optimizing the efficiency of computational algorithms used in solving systems of linear algebraic equations (SLAE). Design / Method / Approach. The work is based on a comprehensive analysis of the functional capabilities of SIMD (Single Instruction, Multiple Data) instructions and their adaptation to classical SLAE. The methodology includes an assessment of the impact of vectorization on the performance and reliability of numerical algorithms across different problem scales. Findings. Innovative versions of classical algorithms for solving SLAE have been developed, characterized by a significant increase in performance while maintaining calculation accuracy. The developed approach ensures efficient vectorization of computations, leading to a significant reduction in the number of iterations and acceleration of algorithm execution. Theoretical Implications. The research expands the theoretical foundation regarding the possibilities of optimizing numerical methods for solving SLAE through data-level parallelism, offering new conceptual principles to enhance computational efficiency. Practical Implications. Optimized algorithms find wide application in various fields where computational efficiency is critical, including engineering calculations, computer graphics, and machine learning. Originality / Value. The work offers an innovative perspective on the modernization of traditional methods for solving SLAE by integrating modern parallel computing technologies, opening up prospects for the development of numerical methods in the context of contemporary computing systems. Research Limitations / Future Research. The research focuses on specific methods and may not cover all aspects of the application of SIMD instructions for other numerical methods. Promising directions for further research include extending the proposed approach to other algorithms and assessing its effectiveness for a broader range of problems.