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Projection algorithms for solving convex feasibility problems
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DOI：10.1137/S0036144593251710.png)
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Abstract
En 中文
Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.
Keywords:
angle between two subspaces
averaged mapping
Cimmino's method
computerized tomography
convex feasibility problem
convex function
convex inequalities
convex programming
convex set
Fejer monotone sequence
firmly nonexpansive mapping
Hilbert space
image recovery
iterative method
Kaczmarz's method
linear convergence
linear feasibility problem
linear inequalities
nonexpansive mapping
orthogonal projection
projection algorithm
projection method
Slater point
subdifferential
subgradient
subgradient algorithm
successive projections
Journal
IF:
6.1
Papers:
888
Citations:
1.2W
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