Mathematical Methods in the Applied Sciences, Vol. , No. 17, (2019) 5687-5695.
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.