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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 Equations with linear operators (numerical methods) 65J20 Improperly posed problems; regularization (numerical methods in abstract spaces) 47A52 Ill-posed problems, regularization
##### References:
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