APPLICATION OF SIMD-INSTRUCTIONS TO INCREASE THE EFFICIENCY OF NUMERICAL METHODS FOR SOLVING SLAE

Abstract

Computational efficiency has become a key factor in progress across many fields of science and technology. However, traditional methods for improving the performance of computational systems have reached their limits, necessitating the search for new approaches to algorithm optimization. This paper explores the application of SIMD instructions to enhance the efficiency of numerical methods for solving systems of linear algebraic equations, particularly the Gauss method and the conjugate gradient method. The proposed approach enables the vectorization of computations, significantly reducing the number of iterative steps and accelerating algorithm execution. An optimization mechanism is presented, based on an analysis of the capabilities of SIMD instructions and their integration into existing SLAE-solving algorithms. The research includes an examination of the impact of vectorization on the performance and stability of numerical algorithms for problems of varying size, as well as a theoretical justification of the proposed approach’s effectiveness. The outcome of this work is the development of optimized versions of the Gauss and conjugate gradient methods, which demonstrate significant performance gains without loss of calculation accuracy. The proposed approach opens new perspectives for further development and improvement of numerical methods within the context of modern computing architectures, with broad applicability in engineering calculations, computer graphics, machine learning, and other fields where computational efficiency is of high priority.