INVERSE BOUNDARY VALUE PROBLEM (ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ, 2025)
This article discusses the steepest descent algorithm of the gradient method used to solve systems of linear algebraic equations. The method for finding the solution by minimizing a functional is explained step-by-step. Theoretical foundations based on gradient and error vectors are presented. A practical example involving a system of four equations is solved using Python, 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.