Supplementary directional relaxations for the acceleration of Kaczmarz's projection method
Starting from an extension of Kaczmarz's method, obtained by us in a previous paper, we introduce new directions for projections. We prove that by this, we don't modify the set of limit points of the original extended Kaczmarz algorithm. For the class of boundary value problems or integra...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2003-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/739 |
| _version_ | 1818006773078949888 |
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| author | Constantin Popa |
| author_facet | Constantin Popa |
| author_sort | Constantin Popa |
| collection | DOAJ |
| description | Starting from an extension of Kaczmarz's method, obtained by us in a previous paper, we introduce new directions for projections. We prove that by this, we don't modify the set of limit points of the original extended Kaczmarz algorithm. For the class of boundary value problems or integral equations of the first kind, we describe a method for constructing these new directions. It is based on considering coarser level of discretization for the initial problem. Some numerical experiments are also presented. |
| first_indexed | 2024-04-14T05:05:47Z |
| format | Article |
| id | doaj.art-ccdc6cef40a149f595d773257b285386 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-14T05:05:47Z |
| publishDate | 2003-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-ccdc6cef40a149f595d773257b2853862022-12-22T02:10:41ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2003-02-01321Supplementary directional relaxations for the acceleration of Kaczmarz's projection methodConstantin Popa0“OVIDIUS” University, Constanta, RomaniaStarting from an extension of Kaczmarz's method, obtained by us in a previous paper, we introduce new directions for projections. We prove that by this, we don't modify the set of limit points of the original extended Kaczmarz algorithm. For the class of boundary value problems or integral equations of the first kind, we describe a method for constructing these new directions. It is based on considering coarser level of discretization for the initial problem. Some numerical experiments are also presented.https://ictp.acad.ro/jnaat/journal/article/view/739least-squares problemsKaczmarz's projection algorithmsupplementary projections |
| spellingShingle | Constantin Popa Supplementary directional relaxations for the acceleration of Kaczmarz's projection method Journal of Numerical Analysis and Approximation Theory least-squares problems Kaczmarz's projection algorithm supplementary projections |
| title | Supplementary directional relaxations for the acceleration of Kaczmarz's projection method |
| title_full | Supplementary directional relaxations for the acceleration of Kaczmarz's projection method |
| title_fullStr | Supplementary directional relaxations for the acceleration of Kaczmarz's projection method |
| title_full_unstemmed | Supplementary directional relaxations for the acceleration of Kaczmarz's projection method |
| title_short | Supplementary directional relaxations for the acceleration of Kaczmarz's projection method |
| title_sort | supplementary directional relaxations for the acceleration of kaczmarz s projection method |
| topic | least-squares problems Kaczmarz's projection algorithm supplementary projections |
| url | https://ictp.acad.ro/jnaat/journal/article/view/739 |
| work_keys_str_mv | AT constantinpopa supplementarydirectionalrelaxationsfortheaccelerationofkaczmarzsprojectionmethod |