A norm convergence result on random products of relaxed projections in Hilbert space

Author:
H. H. Bauschke

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1365-1373

MSC:
Primary 47H09; Secondary 46C99, 47N99, 92C55, 94A12

DOI:
https://doi.org/10.1090/S0002-9947-1995-1257097-1

MathSciNet review:
1257097

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose is a Hilbert space and are closed convex intersecting subsets with projections . Suppose further is a mapping from onto that assumes every value infinitely often. We prove (a more general version of) the following result: If the -tuple is "innately boundedly regular", then the sequence , defined by

Examples without the usual assumptions on compactness are given. Methods of this type have been used in areas like computerized tomography and signal processing.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1257097-1

Keywords:
Banach contraction,
computerized tomography,
convex feasibility problem,
convex programming,
convex set,
Fejér monotone sequence,
Hilbert space,
image reconstruction,
image recovery,
innate bounded regularity,
Kaczmarz's method,
nonexpansive mapping,
orthogonal projection,
projection algorithm,
projection method,
projective mapping,
random product,
relaxation method,
relaxed projection,
signal processing,
unrestricted iteration,
unrestricted product

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© Copyright 1995
American Mathematical Society