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

Grégoire Lecerf (1) , Joelle Saadé (1)

1 Équipe Max

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.

Domaines: Calcul formel [cs.SC]

Grégoire Lecerf, Joelle Saadé. A short survey on Kantorovich-like theorems for Newton's method. 2015. ⟨hal-01196890⟩