Newton Methods with Hölder Derivative

Abstract

The goal of this paper is to establish the rates of convergence of Newton-like methods corresponding to a Hölder continuity assumption on the derivative of the associated nonlinear operator. This generalizes the classical convergence results. Applications are worked out on different kinds of nonlinear integral and differential problems. The abstract general framework is a real or complex Banach space. Applications and computations include a nonlinear boundary value problem and a nonlinear integral equation appearing in mathematical models of radiative transfer. Computations have been done with the only purpose of illustrating how practical convergence respects the theoretical error bounds.

Key Words:

• Nonlinear equations
• Newton-like methods
• Hölder continuity

Mathematics Subject Classification:

• 65J15
• 65L20
• 65R20