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Developing two efficient adaptive Newton‐type methods with memory
Author(s) -
Mohamadi Zadeh Maryam,
Lotfi Taher,
Amirfakhrian Majid
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5381
Subject(s) - convergence (economics) , newton's method , type (biology) , mathematics , class (philosophy) , implementation , index (typography) , order (exchange) , numerical analysis , mathematical optimization , computer science , nonlinear system , mathematical analysis , artificial intelligence , programming language , ecology , physics , quantum mechanics , biology , finance , economics , economic growth
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.