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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| Format: | Article |
| Language: | English |
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Sciendo
2021-05-01
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| Series: | Applied Computer Systems |
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| Online Access: | https://doi.org/10.2478/acss-2021-0007 |
| _version_ | 1819018380626100224 |
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| author | Lavendels Jurijs |
| author_facet | Lavendels Jurijs |
| author_sort | Lavendels Jurijs |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-21T03:18:30Z |
| format | Article |
| id | doaj.art-96ad23ccf425423084329e6651514871 |
| institution | Directory Open Access Journal |
| issn | 2255-8691 |
| language | English |
| last_indexed | 2024-12-21T03:18:30Z |
| publishDate | 2021-05-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Computer Systems |
| spelling | doaj.art-96ad23ccf425423084329e66515148712022-12-21T19:17:46ZengSciendoApplied 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) |
| 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) |
| title | 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_short | Solving Systems of Linear Equations Based on Approximation Solution Projection Analysis |
| title_sort | solving systems of linear equations based on approximation solution projection analysis |
| 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 |