公共不动点问题迭代过程的外推与局部加速
Extrapolation and Local Acceleration of an Iterative Process for Common Fixed Point Problems
摘要：
考虑了希尔伯特空间上一类Cutter算子族的公共不动点问题的序列迭代过程。这些算子具有这样的性质：对于任何点x \inH，通过Tx的法线为x-Tx的超平面总是将空间“切割”成两个半空间，其中一个包含点x，而另一个包含T的（假定非空的）不动点集。定义并研究了广义松弛和广义外推的刀具算子，构造了外推的循环刀具算子。在这个框架中，我们调查的Dos Santos本地加速方法在一个统一的方式，并采用它的组合刀具。为此，我们进行逐次迭代算法的收敛性分析。
英文摘要：
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 x\inH, the hyperplane through Tx whose normal is x-Tx always "cuts" the space into two half-spaces one of which contains the point x while the other contains the (assumed nonempty) fixed point set of T. 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 convergence analysis of successive iteration algorithms.
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