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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:

65J10 Numerical solutions to equations with linear operators
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47A52 Linear operators and ill-posed problems, regularization

Citations:

Zbl 0996.65048
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References:

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