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Approximating curve and strong convergence of the CQ algorithm for the split feasibility problem. (English) Zbl 1189.65107
Summary: Using the idea of Tikhonov’s regularization, we present properties of the approximating curve for the split feasibility problem (SFP) and obtain the minimum-norm solution of SFP as the strong limit of the approximating curve. It is known that in the infinite-dimensional setting, C. Byrne’s [Inverse Probl. 18, No. 2, 441–453 (2002; Zbl 0996.65048)] CQ algorithm (Byrne, 2002) has only weak convergence. We introduce a modification of Byrne’s CQ algorithm in such a way that strong convergence is guaranteed and the limit is also the minimum-norm solution of SFP.

MSC:
65J10Equations with linear operators (numerical methods)
65J20Improperly posed problems; regularization (numerical methods in abstract spaces)
47A52Ill-posed problems, regularization
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