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On two high‐order families of frozen Newton‐type methods
Author(s) -
Amat S.,
Argyros I.,
Busquier S.,
HernándezVerón M. A.
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2126
Subject(s) - mathematics , newton's method , convergence (economics) , order (exchange) , type (biology) , bilinear interpolation , calculus (dental) , algebra over a field , mathematical optimization , nonlinear system , pure mathematics , medicine , ecology , statistics , physics , dentistry , finance , quantum mechanics , economics , biology , economic growth
Summary This paper is devoted to the study of two high‐order families of frozen Newton‐type methods. The methods are free of bilinear operators, which constitute the main limitation of the classical high‐order iterative schemes. Both families are natural generalizations of an efficient third‐order method. Although the methods are more demanding, a semilocal convergence analysis is presented using weaker conditions.