讨论埃特金加速法的收敛性

Study on Aitken's Convergence

埃特金加速法是一种对不动点迭代进行加速的方法,在一些参考资料中仅提出:埃特金加速法只对收敛阶为P=1的迭代函数有加速作用,而对于P>1的情况不一定起作用.本文便要对此问题做出相应的理论分析,而且给予证明.

Aitken is a method to accelerate the iterative method of fixed-point. Some reference books point out that Aitken method can merely have effect on the iterative function of which convergent step is. This article analyzes this question using relative theory, and proves the correction of this problem with changed conditions.