Developing two efficient adaptive Newton‐type methods with memory. (8th November 2018) - Mohamadi Zadeh, Maryam; Lotfi, Taher; Amirfakhrian, Majid
Abstract : In this paper, we derive two general adaptive methods with memory in the class of Newton‐type methods by modifying and introducing one and two self accelerators over a variant of Ostrowski's method. The idea of introducing adaptive self‐accelerator (via all the old information for Newton‐type methods) is new and efficient in order to obtain a higher high efficiency index. Finally, we provide convergence analysis and numerical implementations to show the feasibility and applicability of the proposed methods.