Relaxation parameters and composite refinement techniques
A composite refinement technique for two stationary iterative methods, one of them contains a relaxation parameter, is introduced. Four new techniques, Jacobi successive over relaxation (SOR) composite refinement (RJSOR), SOR Jacobi composite refinement (RSORJ), Gauss–Seidel (GS) SOR composite refin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-08-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037422000267 |
| _version_ | 1817999654799802368 |
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| author | Sh.A. Meligy I.K. Youssef |
| author_facet | Sh.A. Meligy I.K. Youssef |
| author_sort | Sh.A. Meligy |
| collection | DOAJ |
| description | A composite refinement technique for two stationary iterative methods, one of them contains a relaxation parameter, is introduced. Four new techniques, Jacobi successive over relaxation (SOR) composite refinement (RJSOR), SOR Jacobi composite refinement (RSORJ), Gauss–Seidel (GS) SOR composite refinement (RGSSOR) and SOR with GS composite refinement (RSORGS) are compared with their classical forms. The efficient performance of the new forms is well established and confirmed through numerical example. The computational costs and the speed of convergence are considered. The decrease in the required number of iteration is established through the calculation of the spectral radius of the iteration matrices. It is illustrated that the convergence of Jacobi and Gauss–Seidel methods engage the divergence and extend the domain of convergence in the SOR method in the refinement technique. The calculations and graphs are performed by computer algebra system, Mathematica. |
| first_indexed | 2024-04-14T03:11:36Z |
| format | Article |
| id | doaj.art-68a67664180e40f4a6d352e42ec72bfb |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-14T03:11:36Z |
| publishDate | 2022-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-68a67664180e40f4a6d352e42ec72bfb2022-12-22T02:15:35ZengElsevierResults in Applied Mathematics2590-03742022-08-0115100282Relaxation parameters and composite refinement techniquesSh.A. Meligy0I.K. Youssef1Department of Basic Engineering Sciences, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt; Corresponding author.Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt; Department of Mathematics, College of Science, Islamic University, Madinh, Saudi ArabiaA composite refinement technique for two stationary iterative methods, one of them contains a relaxation parameter, is introduced. Four new techniques, Jacobi successive over relaxation (SOR) composite refinement (RJSOR), SOR Jacobi composite refinement (RSORJ), Gauss–Seidel (GS) SOR composite refinement (RGSSOR) and SOR with GS composite refinement (RSORGS) are compared with their classical forms. The efficient performance of the new forms is well established and confirmed through numerical example. The computational costs and the speed of convergence are considered. The decrease in the required number of iteration is established through the calculation of the spectral radius of the iteration matrices. It is illustrated that the convergence of Jacobi and Gauss–Seidel methods engage the divergence and extend the domain of convergence in the SOR method in the refinement technique. The calculations and graphs are performed by computer algebra system, Mathematica.http://www.sciencedirect.com/science/article/pii/S2590037422000267JacobiGauss–SeidelSORRSORJ and RGSSOR methods |
| spellingShingle | Sh.A. Meligy I.K. Youssef Relaxation parameters and composite refinement techniques Results in Applied Mathematics Jacobi Gauss–Seidel SOR RSORJ and RGSSOR methods |
| title | Relaxation parameters and composite refinement techniques |
| title_full | Relaxation parameters and composite refinement techniques |
| title_fullStr | Relaxation parameters and composite refinement techniques |
| title_full_unstemmed | Relaxation parameters and composite refinement techniques |
| title_short | Relaxation parameters and composite refinement techniques |
| title_sort | relaxation parameters and composite refinement techniques |
| topic | Jacobi Gauss–Seidel SOR RSORJ and RGSSOR methods |
| url | http://www.sciencedirect.com/science/article/pii/S2590037422000267 |
| work_keys_str_mv | AT shameligy relaxationparametersandcompositerefinementtechniques AT ikyoussef relaxationparametersandcompositerefinementtechniques |