Modified Hybrid Steepest Method for the Split Feasibility Problem in Image Recovery of Inverse Problems
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Publication Details
Author list: Sitthithakerngkiet K., Deepho J., Kumam P.
Publisher: Taylor and Francis Group
Publication year: 2017
Journal: Numerical Functional Analysis and Optimization (0163-0563)
Volume number: 38
Issue number: 4
Start page: 507
End page: 522
Number of pages: 16
ISSN: 0163-0563
eISSN: 1532-2467
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we regard the CQ algorithm as a fixed point algorithm for averaged mapping, and also try to study the split feasibility problem by the following hybrid steepest method; (Formula presented.) where {αn}⊂(0,1). It is noted that Xu’s original iterative method can conclude only weak convergence. Consequently, we obtain the sequence {xn} generated by our iteration method converges strongly to (Formula presented.), where (Formula presented.) is the unique solution of the variational inequality (Formula presented.) Our result extends and improves the result of Xu, as shown in the literature, from weak to strong convergence theorems. Finally, in the last section, numerical examples for study behavior convergence analysis of this algorithm are obtained. © 2017 Taylor & Francis.
Keywords
CQ algorithm, hybrid steepest method
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