Iterative algorithms with seminorm-induced oblique projections
A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved...
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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/S108533750321201X |
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| _version_ | 1832564937353854976 |
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| author | Yair Censor Tommy Elfving |
| author_facet | Yair Censor Tommy Elfving |
| author_sort | Yair Censor |
| collection | DOAJ |
| description | A definition of oblique projections onto closed convex sets that
use seminorms induced by diagonal matrices which may have zeros
on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal
matrices involved. A block-iterative algorithmic scheme for solving the convex feasibility problem, employing seminorm-induced oblique projections, is constructed and its
convergence for the consistent case is established. The fully simultaneous algorithm converges also in the inconsistent case to the minimum of a certain proximity function. |
| format | Article |
| id | doaj-art-1b83870b38a84ddd8339fed08068f911 |
| 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-1b83870b38a84ddd8339fed08068f9112025-02-03T01:09:42ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-012003738740610.1155/S108533750321201XIterative algorithms with seminorm-induced oblique projectionsYair Censor0Tommy Elfving1Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, IsraelMathematics Department, Linköping University, Linköping SE-581 83, SwedenA definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A block-iterative algorithmic scheme for solving the convex feasibility problem, employing seminorm-induced oblique projections, is constructed and its convergence for the consistent case is established. The fully simultaneous algorithm converges also in the inconsistent case to the minimum of a certain proximity function.http://dx.doi.org/10.1155/S108533750321201X |
| spellingShingle | Yair Censor Tommy Elfving Iterative algorithms with seminorm-induced oblique projections Abstract and Applied Analysis |
| title | Iterative algorithms with seminorm-induced oblique projections |
| title_full | Iterative algorithms with seminorm-induced oblique projections |
| title_fullStr | Iterative algorithms with seminorm-induced oblique projections |
| title_full_unstemmed | Iterative algorithms with seminorm-induced oblique projections |
| title_short | Iterative algorithms with seminorm-induced oblique projections |
| title_sort | iterative algorithms with seminorm induced oblique projections |
| url | http://dx.doi.org/10.1155/S108533750321201X |
| work_keys_str_mv | AT yaircensor iterativealgorithmswithseminorminducedobliqueprojections AT tommyelfving iterativealgorithmswithseminorminducedobliqueprojections |