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On projection algorithms for solving convex feasibility problems. (English) Zbl 0865.47039
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:
47H09Mappings defined by “shrinking” properties
90C25Convex programming
65J10Equations with linear operators (numerical methods)
92C55Biomedical imaging and signal processing, tomography