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Zbl 0865.47039
Bauschke, Heinz H.; Borwein, Jonathan M.
On projection algorithms for solving convex feasibility problems. (English)
[J] SIAM Rev. 38, No.3, 367-426 (1996). ISSN 0036-1445; ISSN 1095-7200/e

Summary: Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion in questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

MSC 2000:: *47H09 Mappings defined by "shrinking" properties
90C25 Convex programming
65J10 Equations with linear operators (numerical methods)
92C55 Tomography

Keywords: angle between two subspaces; averaged mapping; Cimmino's method; convex inequalities; convex programming; convex set; Fejér monotone sequence; firmly nonexpansive mapping; image recovery; Kaczmarz's method; nonexpansive mapping; orthogonal projection; Slater point; subdifferential; subgradient algorithm; successive projections; computerized tomography; convex feasibility problems; quality of convergence

Cited in: Zbl 0990.90094 Zbl 0997.90101 Zbl 0905.47044 Zbl 0898.90099

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