Some modification of Newton’s method by the method of undetermined coefficients
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Authors
Chun, Changbum
Neta, Beny
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
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Date of Issue
2008
Date
2008
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Abstract
In this paper, we construct some modifications of Newton’s method for solving nonlinear equations, which is based on the method of undetermined coefficients. It is shown by way of illustration that the method of undetermined coefficients is a promising tool for developing new methods, and reveals its wide applicability by obtaining some existing methods as special cases. Two new sixth-order methods are developed. Numerical examples are given to support that the methods thus obtained can compete with other iterative methods.
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Description
Computers and Mathematics with Applications, 56, (2008), 2528–2538
The article of record as published may be located at http://dx.doi.org/10.1016/j.camwa.2008.05.005
The article of record as published may be located at http://dx.doi.org/10.1016/j.camwa.2008.05.005
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Applied Mathematics
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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.