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Convergence of the modified CQ algorithm and its application in split feasibility problem. (Chinese. English summary) Zbl 1265.65110
From the summary: In [Inverse Probl. 20, No. 1, 103–120 (2004; Zbl 1051.65067)], the CQ algorithm was proposed by C. Byrne, but only weak convergence was obtained. The purpose of the present paper is to modify his algorithm, so that strong convergence is obtained. The distinction of the paper is that we set a fixed point, add it to the iterative sequence each time. Convergence of the algorithm is thus facilitated. This method has been used in H.-K. Xu’s paper [J. Lond. Math. Soc., II. Ser. 66, No. 1, 240–256 (2002; Zbl 1013.47032)].
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
90C25 Convex programming