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