New families of nonlinear third-order solvers for finding multiple roots
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Authors
Chun, Changbum
Bae, Hwa ju
Neta, Beny
Subjects
Newton's method
Multiple roots
Iterative methods
Order of convergence
Root-finding
Nonlinear equations
Multiple roots
Iterative methods
Order of convergence
Root-finding
Nonlinear equations
Advisors
Date of Issue
2009
Date
2009
Publisher
Elsevier
Language
Abstract
In this paper, we present two new families of iterative methods for multiple roots of nonlinear equations. One of the families require one-function and two-derivative evaluation per step, and the other family requires two-function and one-derivative evaluation. It is shown that both are third-order convergent for multiple roots. Numerical examples suggest that each family member can be competitive to other third-order methods and Newton’s method for multiple roots. In fact the second family is even better than the first.
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Article
Description
Computers and Mathematics with Applications, 57, (2009), 1574–1582, doi: 10.1016/j.camwa.2008.10.070.
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Department
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.