On the radius of convergence of newton's method

Abstract

We present local and semilocal convergence results for Newton's method in a Banach space setting. In particular, using Lipschitz-type assumptions on the second Fréchet-derivative we find results concerning the radius of convergence of Newton's method. Such results are useful in the context of predictor–corrector continuation procedures. Finally, we provide numerical examples to show that our results can apply where earlier ones using Lipschitz assumption on the first Fréchet-derivative fail.

Keywords:

• Newton's method
• Banach space
• Radius of convergence
• Affine invariant operator
• Predictor-corrector procedure

AMS (MOS) Subject Classifications::

• 65B05
• 47H17
• 49D15

C.R. Category::

• G1.5