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Zbl 1189.65107
Wang, Fenghui; Xu, Hong-Kun
Approximating curve and strong convergence of the $CQ$ algorithm for the split feasibility problem. (English)
[J] J. Inequal. Appl. 2010, Article ID 102085, 13 p. (2010). ISSN 1029-242X/e

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, {\it 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 2000:: *65J10 Equations with linear operators (numerical methods)
65J20 Improperly posed problems (numerical methods in abstract spaces)
47A52 Ill-posed problems etc.

Keywords: bounded linear operator; Hilbert space; algorithm; Tikhonov's regularization; split feasibility problem; minimum-norm solution; Byrne's $CQ$ algorithm; strong convergence

Citations: Zbl 0996.65048

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