Ball Convergence for Higher Order Methods Under Weak Conditions (Journal of Mathematical Study, 2021)
We present a local convergence analysis for higher order methods in orderto approximate a locally unique solution of an equation in a Banach space setting. Inearlier studies, Taylor expansions and hypotheses on higher order Fréchet-derivativesare used. We expand the applicability of these methods using only hypotheses on thefirst Fréchet derivative. Moreover, we obtain a radius of convergence and computableerror bounds using Lipschitz constants not given before. Numerical examples are alsopresented in this study.
Keywords: Higher order method; Banach space; Fréchet derivative; local convergence.