关于实李普希兹映射的lshikawa迭代的收敛率和加速收敛问题

Convergence Rate and Acceleration on lshikawa's lterations of Real Lipschitz Mappings

本文研究使用Ｉｓｈｉｋａｗａ迭代格式求实李普希兹映射的不动点，指出该迭代格式仅具线性收敛率；对于参变量序列｛αｎ｝、｛βｎ｝所取的不同的值，比较了迭代格式的收敛速度．在给出加速因子定义的基础上，本文给出了加速收敛的一个充分条件．

In this paper we consider Ishikawa's iteration scheme to find fixed points of real Lipschitz mappings. We declare that the Ishikawa's iteration only has linear convergence rate. For distinct values of sequence {αn} and {βn},we have compared the convergence rate of the iterations. As an important result, an accelerativemethod,which can get more higher convergence rate,is given in this paper.