The purpose and objectives of this work are the improvement of the quality of the iterative solution of systems of linear equations(SLAE). To achieve this in the method associated with multi-level wavelet decomposition of the vector of residuals. Calculations in Matlab mathematical package, has confirmed the adequacy of the proposed method and its capabilities in solving systems of linear algebraic equations.

Keywords: the system of linear equations, wavelet transform, wavelet filter, preconditioning algorithm, algorithm, relative error, vector-function, packet decomposition, the norm of the vector, the condition number

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

The purpose and objectives of this work consist in the development of regularization methods for solving systems of linear equations. For their achievements in this paper we propose a modified least squares method for solving systems of linear equations, which is based on the use of q-differentiation. Calculations based on a test of task performed in Matlab mathematical package, confirmed the adequacy of the method and in some cases have shown its advantage over traditional methods for the regularization of systems of linear equations.

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