A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations
A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/836901 |
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| Summary: | A family of derivative-free methods of seventh-order
convergence for solving nonlinear equations is suggested. In the proposed
methods, several linear combinations of divided differences are used in
order to get a good estimation of the derivative of the given function at
the different steps of the iteration. The efficiency indices of the members of
this family are equal to 1.6266. Also, numerical examples are used to show
the performance of the presented methods, on smooth and nonsmooth
equations, and to compare with other derivative-free methods, including
some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture. |
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| ISSN: | 1085-3375 1687-0409 |