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Image recovery by convex combinations of projections. (English) Zbl 0752.65045
The functional analytic question discussed in this paper is: For which T one has weak convergence of the sequences {T n x} n=0 to a common fixed point of a finite number of projections P 1 ,,P r (onto convex closed subsets C 1 ,,C r ) in a Hilbert space. It is shown via more abstract results that one may choose T=α 0 id+ i=1 r α i T i with T i =id+λ i (P i -id), 0<λ i <2, α j >0, 0 r α j =1. It is argued that this choice is more suitable for parallel computer implementation than the classical T=T r T 1 .

65J10Equations with linear operators (numerical methods)
65Y05Parallel computation (numerical methods)
46C05Hilbert and pre-Hilbert spaces: geometry and topology
47A50Equations and inequalities involving linear operators, with vector unknowns