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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Viewing parallel projection methods as sequential ones in convex feasibility problems

Author: G. Crombez
Journal: Trans. Amer. Math. Soc. 347 (1995), 2575-2583
MSC: Primary 65J05; Secondary 41A65, 65K99
MathSciNet review: 1277105
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Abstract: 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.

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Keywords: Convex set, parallel projection method, sequential projection method, convex feasibility problem, block-iterative projection method
Article copyright: © Copyright 1995 American Mathematical Society