An improvement of the Euler-Chebyshev iterative method (Q819019)
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scientific article; zbMATH DE number 5014220
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An improvement of the Euler-Chebyshev iterative method |
scientific article; zbMATH DE number 5014220 |
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An improvement of the Euler-Chebyshev iterative method (English)
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22 March 2006
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The computation of a simple root of a sufficiently smooth scalar function \(f\) is discussed. The Newton method and the Euler-Chebyshev method are briefly presented. A method based on the Euler-Chebyshev method using a linear combination of function values of \(f\) with a convergence order of 5 is constructed. For the practical test of 13 functions, a Maple-algorithm with iteration depending arithmetic is used.
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Euler-Chebyshev's formula
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nonlinear equation
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iterative methods
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order of convergence
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computational efficiency
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numerical examples
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Newton method
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Maple algorithm
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