<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis

Applied Computer Systems

This work is licensed under the Creative Commons Attribution 4.0 International License.

The paper considers an iterative method for solving systems of linear equations (SLE), which applies multiple displacement of the approximation solution point...

Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis

Published Online: Jun 04, 2021

Page range: 54 - 59

DOI: https://doi.org/10.2478/acss-2021-0007

Keywords
Iterative methods, solution approximation projection, systems of linear equations (SLE)

© 2021 Jurijs Lavendels, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis

Published Online: Jun 04, 2021

Page range: 54 - 59

DOI: https://doi.org/10.2478/acss-2021-0007

KeywordsIterative methods, solution approximation projection, systems of linear equations (SLE)

© 2021 Jurijs Lavendels, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Iterative methods, solution approximation projection, systems of linear equations (SLE)