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Viewing parallel projection methods as sequential ones in convex feasibility problems. (English) Zbl 0846.46010
Summary: We show that the parallel projection method with variable weights and one variable relaxation coefficient for obtaining a point in the intersection of a finite number of closed convex sets in a given Hilbert space may be interpreted as a semi-alternating sequential projection method in a suitably newly constructed Hilbert space. As such, convergence results for the parallel projection method may be derived from those which may be constructed in the semi-alternating sequential case.

MSC:
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
68U10 Computing methodologies for image processing
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