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The strong convergence of a KM-CQ-like algorithm for a split feasibility problem. (English) Zbl 1211.65065
Let C and Q be nonempty closed convex subsets of the real Hilbert spaces H 1 and H 2 , respectively, and let A:H 1 H 2 be a bounded linear operator. The split feasibility problem is to find a point x satisfying xC, AxQ, if such point exists. For solving the problem, the authors suggest a strongly convergent algorithm which combines the CQ-method x k+1 =P C (I-γA T (I-P Q )A)x k , 0<γ<2/ρ(A T A) with the Krasnosel’skii-Mann (KM) iterative process x k+1 =(1-α k )x k +α k Tx k , α k (0,1), where T is a nonexpansive operator.

65J22Inverse problems (numerical methods in abstract spaces)
65J10Equations with linear operators (numerical methods)
47A50Equations and inequalities involving linear operators, with vector unknowns