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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 |

### Keywords:

convex feasibility problem; block-iterative projection method; parallel projection method with variable weights; one variable relaxation coefficient; intersection of a finite number of closed convex sets in a given Hilbert space; semi-alternating sequential projection method
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\textit{G. Crombez}, Trans. Am. Math. Soc. 347, No. 7, 2575--2583 (1995; Zbl 0846.46010)

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### References:

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