多点New ton-Raphson迭代的新几何解释

The new geometric explanation of multipoint Newton-Raphson iteration

正如"线性化"揭示了Newton迭代的构造思想一样,本文给出的一种几何解释揭示了多点Newton-Raphson迭代的构造思想,由此我们能够给出它的4阶收敛速度的一个简单证明,以及相关的一些重要结果.此外,我们还将多点Newton-Raphson迭代与Olver迭代、Newton迭代进行了综合比较,结论是:多点Newton-Raphson迭代更实用.

In this paper,we give a new geometric explanation of the multipoint Newton-Raphson iteration. According to this explanation,we give a simple proof of its 4-order convergence and some related results. In addition, we conclude that the multipoint Newton-Raphson iteration is more efficient than the Olver iteration and the Newton iteration.