Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces
Abstract The split equality problem is a generalization of the split feasibility problem, meanwhile it is a special case of multiple-sets split equality problems. In this paper, we propose an iterative algorithm for solving the multiple-sets split equality problem whose iterative step size is split...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-0982-7 |
| _version_ | 1818317359216066560 |
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| author | Dianlu Tian Luoyi Shi Rudong Chen |
| author_facet | Dianlu Tian Luoyi Shi Rudong Chen |
| author_sort | Dianlu Tian |
| collection | DOAJ |
| description | Abstract The split equality problem is a generalization of the split feasibility problem, meanwhile it is a special case of multiple-sets split equality problems. In this paper, we propose an iterative algorithm for solving the multiple-sets split equality problem whose iterative step size is split self-adaptive. The advantage of the split self-adaptive step size is that it could be obtained directly from the iterative procedure without needing to have any information of the spectral norm of the related operators. Under suitable conditions, we establish the theoretical convergence of the algorithm proposed in Hilbert spaces, and several numerical results confirm the effectiveness of the algorithm proposed. |
| first_indexed | 2024-12-13T09:36:04Z |
| format | Article |
| id | doaj.art-5666f198ada64682ba76544da1c43b3f |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T09:36:04Z |
| publishDate | 2016-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-5666f198ada64682ba76544da1c43b3f2022-12-21T23:52:21ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-01-01201611910.1186/s13660-016-0982-7Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spacesDianlu Tian0Luoyi Shi1Rudong Chen2Department of Mathematics, Tianjin Polytechnic UniversityDepartment of Mathematics, Tianjin Polytechnic UniversityDepartment of Mathematics, Tianjin Polytechnic UniversityAbstract The split equality problem is a generalization of the split feasibility problem, meanwhile it is a special case of multiple-sets split equality problems. In this paper, we propose an iterative algorithm for solving the multiple-sets split equality problem whose iterative step size is split self-adaptive. The advantage of the split self-adaptive step size is that it could be obtained directly from the iterative procedure without needing to have any information of the spectral norm of the related operators. Under suitable conditions, we establish the theoretical convergence of the algorithm proposed in Hilbert spaces, and several numerical results confirm the effectiveness of the algorithm proposed.http://link.springer.com/article/10.1186/s13660-016-0982-7split self-adaptive step sizemultiple-sets split equality problemiterate algorithm |
| spellingShingle | Dianlu Tian Luoyi Shi Rudong Chen Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces Journal of Inequalities and Applications split self-adaptive step size multiple-sets split equality problem iterate algorithm |
| title | Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces |
| title_full | Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces |
| title_fullStr | Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces |
| title_full_unstemmed | Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces |
| title_short | Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces |
| title_sort | iterative algorithm for solving the multiple sets split equality problem with split self adaptive step size in hilbert spaces |
| topic | split self-adaptive step size multiple-sets split equality problem iterate algorithm |
| url | http://link.springer.com/article/10.1186/s13660-016-0982-7 |
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