迭代法加速 数值分析论文 数值分析大作业 数值分析

迭代法加速（数值分析创新大作业）（论文） Steffensen’s acceleration and Aitkan’s acceleration We have learned the Fixed point iterative method, but we found that this method is linearly convergent, sometimes it’s even divergence,and some iterated function is divergence. Through the data access,I found two ways of accelerating the iterative method,following I would introduce these methods. 1. Aitkan’s acceleration Suppose = ,through  mean value theorem of intergrals, we have - = ( - ),  and is between and . Suppose = , = ,  and = , we  have - ,  and = , So we have the sequence{ } = , = , = ,(k=0,1,2,…) That’s called Aitkan’s iterative method,due to (0