The purpose and objectives of this work is to develop methods of iterative methods for solving systems of linear equations. Achieving the goals and objectives achieved by the development of an iterative method using the apparatus q-differentiation. With the software package Matlab Computational experiments, which resulted in the performance of the proposed method is confirmed.

Keywords: system of linear equations, the objective function, the gradient method, iterative method, modeling, algorithm, function extremum, q-derivative, relative error, norm of the vector, the conditionality of the problem