Updated and Weaker Convergence Criteria of Newton Iterates for Equations

Abstract

Newton iteration is often used as a solver for nonlinear equations in abstract spaces. Some of the main concerns are general: Criteria for convergence, error estimations on consecutive iterates, and the location of a solution. A plethora of authors has addressed these concerns by presenting results based on the celebrated Kantorovich theory. This article contributes in this direction by extending earlier results but without additional conditions. These extensions become possible using a more precise majorization than the one given in earlier articles. Numerical experimentation complements the theoretical results involving a partial differential and an integral equation.