Some optimal iterative methods and their with memory variants (Q392252)
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scientific article; zbMATH DE number 6244751
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some optimal iterative methods and their with memory variants |
scientific article; zbMATH DE number 6244751 |
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Some optimal iterative methods and their with memory variants (English)
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13 January 2014
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The paper concerns some optimal iterative methods for solving nonlinear equations. Based on some existing works, the author constructs a new method, which needs only 4 function evaluations per step and achieves the optimal 8th-order accuracy. This result is also proved rigorously. Furthermore, by carefully choosing the free parameter in the method, the author obtains a new method with memory and obtains a much better convergence rate, namely, order 10. Numerical results are presented to confirm the theoretical results.
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weight function
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\(R\)-order
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high precision computing
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iterative method
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nonlinear equation
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method with memory
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convergence
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numerical result
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