An iterative approach to a constrained least squares problem
A constrained least squares problem in a Hilbert space H is considered. The standard Tikhonov regularization method is used. In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of H, an iterative algorithm is designed. The result...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503212082 |
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| _version_ | 1849308632828608512 |
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| author | Simeon Reich Hong-Kun Xu |
| author_facet | Simeon Reich Hong-Kun Xu |
| author_sort | Simeon Reich |
| collection | DOAJ |
| description | A constrained least squares problem in a Hilbert space H is considered. The standard Tikhonov regularization method is used.
In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of H, an iterative algorithm is designed. The resulting sequence is shown to converge strongly to the unique solution of the regularized problem. The net of the solutions to the regularized problems strongly converges to the minimum norm solution of the least squares problem if its solution set is nonempty. |
| format | Article |
| id | doaj-art-0dbe77e1569f4ca8b67ee8a2abe6e4b2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0dbe77e1569f4ca8b67ee8a2abe6e4b22025-08-20T03:54:24ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-012003850351210.1155/S1085337503212082An iterative approach to a constrained least squares problemSimeon Reich0Hong-Kun Xu1Department of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, IsraelDepartment of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South AfricaA constrained least squares problem in a Hilbert space H is considered. The standard Tikhonov regularization method is used. In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of H, an iterative algorithm is designed. The resulting sequence is shown to converge strongly to the unique solution of the regularized problem. The net of the solutions to the regularized problems strongly converges to the minimum norm solution of the least squares problem if its solution set is nonempty.http://dx.doi.org/10.1155/S1085337503212082 |
| spellingShingle | Simeon Reich Hong-Kun Xu An iterative approach to a constrained least squares problem Abstract and Applied Analysis |
| title | An iterative approach to a constrained least squares problem |
| title_full | An iterative approach to a constrained least squares problem |
| title_fullStr | An iterative approach to a constrained least squares problem |
| title_full_unstemmed | An iterative approach to a constrained least squares problem |
| title_short | An iterative approach to a constrained least squares problem |
| title_sort | iterative approach to a constrained least squares problem |
| url | http://dx.doi.org/10.1155/S1085337503212082 |
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