Construction of optimal order nonlinear solvers using inverse interpolation
Authors
Neta, Beny
Petkovic, M.S.
Subjects
Multipoint iterative methods
Nonlinear equations
Optimal order of convergence
Inverse interpolation
Nonlinear equations
Optimal order of convergence
Inverse interpolation
Advisors
Date of Issue
2010
Date
2010
Publisher
Language
Abstract
There is a vast literature on finding simple roots of nonlinear equations by iterative meth- ods. These methods can be classified by order, by the information used or by efficiency. There are very few optimal methods, that is methods of order 2m requiring m + 1 function evaluations per iteration. Here we give a general way to construct such methods by using inverse interpolation and any optimal two-point method. The presented optimal multi- point methods are tested on numerical examples and compared to existing methods of the same order of convergence.
Type
Description
Applied Mathematics and Computation, 217, (2010), 2448-2455.
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2010.07.045
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2010.07.045
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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.