Olver迭代与Newton迭代的比较

Comparison Investigation Between Olver Iteration and Newton Iteration

lver迭代是一个立方收敛的求根公式 ,而Newton迭代仅是平方收敛 ,但前者却不如后者为人们所熟知 ,以至于近来有作者称其推导了一个新的高阶迭代公式 ,而实际就是Olver迭代公式却浑然不知。那么 ,到底是什么原因导致Olver迭代没有被广大的计算方法教科书介绍呢 ?本文对Newton迭代与Olver迭代做了详尽的分析 ,给出了两者各自的精度表达式 ,并对两者进行了比较 ,结论是 :从计算效率及精度方面综合考虑 。

Olver iteration is a formula for solving root with the cubicle convergence and Newton iteration is one with the square convergence. But only Newton iteration i s introduced extensively in textbooks, and few people know Olver iteration. Why? In the paper, Newton iteration and Olver iteration are analyzed in detail and t he expressions of accuracy of the two iterations are derived. By comparing the a nswer, it is found that Newton iteration is better than Olver iteration if compu tational efficiency and accuracy are considered synthetically.