Certain improvements of Newton’s method with fourth-order convergence
Authors
Chun, Changbum
Neta, Beny
Advisors
Second Readers
Subjects
Newton's method
Iterative methods
Nonlinear equations
Order of convergence
Method of undetermined coefficients
Root-finding methods
Iterative methods
Nonlinear equations
Order of convergence
Method of undetermined coefficients
Root-finding methods
Date of Issue
2009
Date
Publisher
Language
Abstract
In this paper we present two new schemes, one is third-order and the other is fourth-order.
These are improvements of second-order methods for solving nonlinear equations and are
based on the method of undetermined coefficients. We show that the fourth-order method
is more efficient than the fifth-order method due to Kou et al. [J. Kou, Y. Li, X. Wang, Some
modifications of Newton’s method with fifth-order covergence, J. Comput. Appl. Math., 209
(2007) 146–152]. Numerical examples are given to support that the methods thus obtained
can compete with other iterative methods.
Type
Article
Description
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2009.06.007
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funding
Format
Citation
Applied Mathematics and Computation, Volume 215, (2009), pp. 821–828
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.