INVERSE BOUNDARY VALUE PROBLEM
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Gradient method, steepest descent, iterative method, symmetric matrix, positive definiteness, functional, optimization, Python, algorithm, error vector.##article.abstract##
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.
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