Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces
<p>The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we...
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| Format: | Article |
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| Language: | English |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/84919 |
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| collection | DOAJ |
| description | <p>The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.</p> |
| format | Article |
| id | doaj-art-8ce4d34ec48e4b438e278bf9d0083076 |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8ce4d34ec48e4b438e278bf9d00830762025-02-03T01:29:00ZengWileyAbstract and Applied Analysis1085-33752006-01-012006Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces<p>The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.</p>http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/84919 |
| spellingShingle | Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces Abstract and Applied Analysis |
| title | Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces |
| title_full | Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces |
| title_fullStr | Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces |
| title_full_unstemmed | Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces |
| title_short | Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces |
| title_sort | bregman distances totally convex functions and a method for solving operator equations in banach spaces |
| url | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/84919 |