Developing two efficient adaptive Newton‐type methods with memory. (8th November 2018)

• Record Type: Journal Article
• Authors: Mohamadi Zadeh, Maryam; Lotfi, Taher; Amirfakhrian, Majid
• Other Names: Vigo-Aguiar Jesus guestEditor.; Kumam Poom guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 17(2019)
• Page Start: 5687
• Page End: 5695
• Publication Date: 2018-11-08
• Subjects: adaptive method -- convergence order -- efficiency index -- Hermite's interpolation -- iterative methods -- method without and with memory -- onlinear equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5381
• Languages: English
• ISSNs: 0170-4214

Abstract

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.