Block-iterative algorithms for solving convex feasibility problems in Hilbert and in Banach spaces

We establish convergence theorems for two different block-iterative methods for solving the problem of finding a point in the intersection of the fixed point sets of a finite number of nonexpansive mappings in Hilbert and in finite-dimensional Banach spaces, respectively.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 343; no. 1; pp. 427 - 435
Main Authors: Aleyner, Arkady, Reich, Simeon
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.07.2008
Elsevier
Subjects:
Block-iterative algorithmic scheme
Common fixed point
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Nonexpansive mapping
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Relaxation method
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Relaxation method
Block-iterative algorithmic scheme
Common fixed point
Nonexpansive mapping
Fix point
Mathematical analysis
Algorithmics
Problem solving
Iterative method
Banach space
Algorithm
Application
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Description
Summary:We establish convergence theorems for two different block-iterative methods for solving the problem of finding a point in the intersection of the fixed point sets of a finite number of nonexpansive mappings in Hilbert and in finite-dimensional Banach spaces, respectively.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.01.087