On a bi-parametric class of optimal eighth-order derivative-free methods (Q2896980)
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scientific article; zbMATH DE number 6053400
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a bi-parametric class of optimal eighth-order derivative-free methods |
scientific article; zbMATH DE number 6053400 |
Statements
5 July 2012
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nonlinear scalar equations
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optimality
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order of convergence
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derivate-free methods
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simple root
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without memory iterations
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Newton's method
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Steffensen's method
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numerical examples
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On a bi-parametric class of optimal eighth-order derivative-free methods (English)
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Given a nonlinear equation of one variate \(f(x)=0\). There are many well-known methods of finding the solution of the equation. Among them are Newton's method and Steffensen's method. A new three-step derivative-free class of eighth-order methods is proposed in the paper. Optimality conditions of these methods are established. Numerical examples that illustrate the proposed methods are given at the end of the article.
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