On the complexity of convergence for high order iterative methods

Abstract

Lipschitz-type conditions on the second derivative or conditions on higher than two derivatives not appearing on these methods have been employed to prove convergence. But these restrictions limit the applicability of high convergence order iterative methods although they may converge. That is why a new semi-local analysis is presented using only information taken from the derivatives on these methods. The new results compare favorably to the earlier ones even if the earlier conditions are used, since the latter use tighter Lipschitz parameters. Special cases and applications test convergence criteria. © 2022 Elsevier Inc.