Global convergence of Newton's method on an interval (Q1880264)
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scientific article; zbMATH DE number 2101619
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global convergence of Newton's method on an interval |
scientific article; zbMATH DE number 2101619 |
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Global convergence of Newton's method on an interval (English)
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22 September 2004
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Global convergence of the Newton-Raphson method for a scalar equation \(f(x)=0 \) is studied in terms of conditions on \(f\) of the form \[ f(b)>f(a)\text{ implies }f^{\prime }(a)+f^{\prime }(b)>\frac{f(b)-f(a)}{b-a}, \] which are then applied for the case of Kepler's equation, to illustrate their effectiveness.
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Newton-Raphson method
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global convergence
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Kepler's equation
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