On some extensions of the accelerated overrelaxation (AOR) theory
This paper extends the convergence theory of the Accelerated Overrelaxation (AOR) method to cases analogous to those considered first by Ostrowski and then by Varga in connection with the Successive Overrelaxation (SOR) method. Among others, the Ostrowski Theorem, some of the theorems by Varga on th...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000064 |
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| _version_ | 1832562080283099136 |
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| author | A. Hadjidimos A. Yeyios |
| author_facet | A. Hadjidimos A. Yeyios |
| author_sort | A. Hadjidimos |
| collection | DOAJ |
| description | This paper extends the convergence theory of the Accelerated Overrelaxation (AOR) method to cases analogous to those considered first by Ostrowski and then by Varga in connection with the Successive Overrelaxation (SOR) method. Among others, the Ostrowski Theorem, some of the theorems by Varga on the extensions of the SOR theory, and some recent results by Niethammer and by the authors are obtained as special cases of the work presented in this paper. In addition, several points are raised which suggest further research. |
| format | Article |
| id | doaj-art-d6ead6db3c1c46318cbd8b9b83e3902f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d6ead6db3c1c46318cbd8b9b83e3902f2025-02-03T01:23:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-0151496010.1155/S0161171282000064On some extensions of the accelerated overrelaxation (AOR) theoryA. Hadjidimos0A. Yeyios1Department of Mathematics, University of loannina, loannina, GreeceDepartment of Mathematics, University of loannina, loannina, GreeceThis paper extends the convergence theory of the Accelerated Overrelaxation (AOR) method to cases analogous to those considered first by Ostrowski and then by Varga in connection with the Successive Overrelaxation (SOR) method. Among others, the Ostrowski Theorem, some of the theorems by Varga on the extensions of the SOR theory, and some recent results by Niethammer and by the authors are obtained as special cases of the work presented in this paper. In addition, several points are raised which suggest further research.http://dx.doi.org/10.1155/S0161171282000064three-part splittingsfirst order iterative methodsecond order iterative methodsuccessive overrelaxation (SOR) methodextrapolationaccelerated overrelaxation (AOR) method. |
| spellingShingle | A. Hadjidimos A. Yeyios On some extensions of the accelerated overrelaxation (AOR) theory International Journal of Mathematics and Mathematical Sciences three-part splittings first order iterative method second order iterative method successive overrelaxation (SOR) method extrapolation accelerated overrelaxation (AOR) method. |
| title | On some extensions of the accelerated overrelaxation (AOR) theory |
| title_full | On some extensions of the accelerated overrelaxation (AOR) theory |
| title_fullStr | On some extensions of the accelerated overrelaxation (AOR) theory |
| title_full_unstemmed | On some extensions of the accelerated overrelaxation (AOR) theory |
| title_short | On some extensions of the accelerated overrelaxation (AOR) theory |
| title_sort | on some extensions of the accelerated overrelaxation aor theory |
| topic | three-part splittings first order iterative method second order iterative method successive overrelaxation (SOR) method extrapolation accelerated overrelaxation (AOR) method. |
| url | http://dx.doi.org/10.1155/S0161171282000064 |
| work_keys_str_mv | AT ahadjidimos onsomeextensionsoftheacceleratedoverrelaxationaortheory AT ayeyios onsomeextensionsoftheacceleratedoverrelaxationaortheory |