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

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277105-1

MathSciNet review:
1277105

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277105-1

Keywords:
Convex set,
parallel projection method,
sequential projection method,
convex feasibility problem,
block-iterative projection method

Article copyright:
© Copyright 1995
American Mathematical Society