THE GRADIENT(MOST OFTEN SALTWORKS) METHOD (ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ, 2025)
This paper discusses the steepest descent algorithm of the gradient method used to solve systems of linear algebraic equations. The method of finding the solution of the system by minimizing a functional is explained step by tep. The theoretical foundations of the iterative approach based on gradient and error vectors are presented. As an example, a system of four-variable equations is solved using the Python programming environment, and the convergence rate and accuracy of the algorithm are demonstrated. The results show that the gradient method is a simple and efficient computational tool suitable for solving large-scale linear systems.