对牛顿方法的Kantorovich类定理的简要概述

ACM Commun. Comput. Algebra Pub Date : 2016-04-27 DOI:10.1145/2930964.2930965

Grégoire Lecerf, Joelle Saadé

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引用次数: 2

摘要

研究了Banach空间上连续可微映射的Newton迭代器向单根收敛性的一些有影响的定量结果。本文给出了坎托罗维奇定理的一般表述，并从头开始给出了简明的证明，以飨广大读者。从中，我们可以快速恢复已知的结果，并收集历史笔记以及最近文章的指针。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A short survey on Kantorovich: like theorems for Newton's method

We survey influential quantitative results on the convergence of the Newton iterator towards simple roots of continuously differentiable maps defined over Banach spaces. We present a general statement of Kantorovich's theorem, with a concise proof from scratch, dedicated to wide audience. From it, we quickly recover known results, and gather historical notes together with pointers to recent articles.

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ACM Commun. Comput. Algebra

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