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Zbl 1080.65033
Qu, Biao; Xiu, Naihua
A note on the $CQ$ algorithm for the split feasibility problem.
(English)
[J] Inverse Probl. 21, No. 5, 1655-1665 (2005). ISSN 0266-5611

The authors present modifications to the $CQ$ algorithm proposed by {\it Ch. Byrne} [Inverse Probl. 18, No. 2, 441--453 (2002; Zbl 0996.65048)] and to the relaxed $CQ$ algorithm proposed by {\it Q. Z. Yang} [Inverse Probl. 20, 1261--1266 (2004; Zbl 1066.65047)] to solve the split feasibility problem $x^{k+1}=P_C(x^k-yA^T(P_Q-I)Ax^k)$ by adopting Armijo-like searches. The modified algorithm need not compute matrix inverses and the largest eigenvalue of the matrix $A^TA$. It provides a sufficient decrease of the objective function at each iteration by a judicious choice of the stepsize and can identify the existence of solutions by the iterative sequence. The convergence of the modified algorithms is established under mild conditions.
[Rémi Vaillancourt (Ottawa)]
MSC 2000:
*65F30 Other matrix algorithms
65F10 Iterative methods for linear systems

Keywords: iterative oblique projection; split feasibility problem; $CQ$ algorithm; convergence

Citations: Zbl 0996.65048; Zbl 1066.65047

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