Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 102085, 13 pages
doi:10.1155/2010/102085
Research Article

Approximating Curve and Strong Convergence of the CQ Algorithm for the Split Feasibility Problem

Fenghui Wang1,2 and Hong-Kun Xu3

1Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
2Department of Mathematics, Luoyang Normal University, Luoyang 471022, China
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan

Received 14 December 2009; Accepted 14 January 2010

Academic Editor: Yeol Je Cho

Copyright © 2010 Fenghui Wang and Hong-Kun Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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, Byrne's 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.