Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis

Abstract The paper considers an iterative method for solving systems of linear equations (SLE), which applies multiple displacement of the approximation solution point in the direction of the final solution, simultaneously reducing the entire residual of the system of equations. The method reduces the requirements for the matrix of SLE. The following SLE property is used: the point is located farther from the system solution result compared to the point projection onto the equation. Developing the approach, the main emphasis is made on reduction of requirements towards the matrix of the system of equations, allowing for higher volume of calculations.