Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis

Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis

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 requir...

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Main Author: Lavendels Jurijs
Format: Article
Language:English
Published: Sciendo 2021-05-01
Series:Applied Computer Systems
Subjects:
iterative methods
solution approximation projection
systems of linear equations (sle)
Online Access:https://doi.org/10.2478/acss-2021-0007
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spelling doaj-96ad23ccf425423084329e66515148712021-09-06T19:41:01ZengSciendoApplied Computer Systems2255-86912021-05-01261545910.2478/acss-2021-0007Solving Systems of Linear Equations Based on Approximation Solution Projection AnalysisLavendels Jurijs0Riga Technical University, Riga, LatviaThe 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.https://doi.org/10.2478/acss-2021-0007iterative methodssolution approximation projectionsystems of linear equations (sle)
collection DOAJ
language English
format Article
sources DOAJ
author Lavendels Jurijs
spellingShingle Lavendels Jurijs
Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis
Applied Computer Systems
iterative methods
solution approximation projection
systems of linear equations (sle)
author_facet Lavendels Jurijs
author_sort Lavendels Jurijs
title Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis
title_short Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis
title_full Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis
title_fullStr Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis
title_full_unstemmed Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis
title_sort solving systems of linear equations based on approximation solution projection analysis
publisher Sciendo
series Applied Computer Systems
issn 2255-8691
publishDate 2021-05-01
description 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.
topic iterative methods
solution approximation projection
systems of linear equations (sle)
url https://doi.org/10.2478/acss-2021-0007
work_keys_str_mv AT lavendelsjurijs solvingsystemsoflinearequationsbasedonapproximationsolutionprojectionanalysis
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