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Zbl 1080.65035
Zhao, Jinling; Yang, Qingzhi
Several solution methods for the split feasibility problem. (English)
[J] Inverse Probl. 21, No. 5, 1791-1799 (2005). ISSN 0266-5611

The authors generalize the Krasnoselskii-Mann theorem and present several algorithms to solve the split feasibility problem (SFP) $x^{k+1}=P_C(x^k-yA^T(I-P_Q)Ax^k)$ in case the projections $P_C$ and $P_Q$ of the algorithm proposed by {\it Ch. Byrne} [Inverse Probl. 18, No. 2, 441-453 (2002; Zbl 0996.65048)], are difficult or even impossible to compute. A perturbed projection method based on the $CQ$ algorithm and an inverse method based on Mosco-convergence of sets are presented to solve the SFP and the convergence of these algorithms is established. An new efficient conjugate gradient method is used to make the algorithms more practical and easier to implement.
[Rémi Vaillancourt (Ottawa)]

MSC 2000:: *65F30 Other matrix algorithms
65F10 Iterative methods for linear systems

Keywords: iterative oblique projection; split feasibility problem; Krasnoselskii-Mann theorem; algorithms; $CQ$ algorithm; inverse method; convergence; conjugate gradient method

Citations: Zbl 0996.65048

Cited in: Zbl 1256.65052 Zbl 1232.49017

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