Extrapolation and local acceleration of an iterative process for common fixed point problems

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• 作者：Andrzej Cegielski^a ; ^{a.cegielski@wmie.uz.zgora.pl} ; Yair Censor^b ; ^{yair@math.haifa.ac.il}
• 关键词：Common fixed point ; Cyclic projection method ; Cutter operator ; Quasi-nonexpansive operators ; Dos Santos local acceleration
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：15 October, 2012
• 卷：394
• 期：2
• 页码：809-818
• 文件大小：244 K

摘要

We consider sequential iterative processes for the common fixed point problem of families of cutter operators on a Hilbert space. These are operators that have the property that, for any point , the hyperplane through whose normal is always 鈥渃uts鈥澛爐he space into two half-spaces, one of which contains the point while the other contains the (assumed nonempty) fixed point set of . We define and study generalized relaxations and extrapolation of cutter operators, and construct extrapolated cyclic cutter operators. In this framework we investigate the Dos Santos local acceleration method in a unified manner and adopt it to a composition of cutters. For these, we conduct a convergence analysis of successive iteration algorithms.