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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 149508, 12 pages
http://dx.doi.org/10.1155/2012/149508
Research Article

An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem

1School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
2School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

Received 29 December 2011; Revised 23 February 2012; Accepted 23 February 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Yazheng Dang and Yan Gao. 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

The multiple-set split feasibility problem (MSSFP), as a generalization of the split feasibility problem, is to find a point in the intersection of a family of closed convex sets in one space such that its image under a linear transformation will be in the intersection of another family of closed convex sets in the image space. Censor et al. (2005) proposed a method for solving the multiple-set split feasibility problem (MSSFP), whose efficiency depends heavily on the step size, a fixed constant related to the Lipschitz constant of which may be slow. In this paper, we present an accelerated algorithm by introducing an extrapolated factor to solve the multiple-set split feasibility problem. The framework encompasses the algorithm presented by Censor et al. (2005). The convergence of the method is investigated, and numerical experiments are provided to illustrate the benefits of the extrapolation.