On zero finding methods of higher order from data at one point (Q1122311)
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scientific article; zbMATH DE number 4106137
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On zero finding methods of higher order from data at one point |
scientific article; zbMATH DE number 4106137 |
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On zero finding methods of higher order from data at one point (English)
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1989
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The author generalizes to higher order methods the approach of \textit{S. Smale} [The merging of disciplines in pure, applied and computational mathematics 185-196 (1986; Zbl 0613.65058)] for the convergence analysis of iterative methods for analytic functions based on data at one point. A particular aim is here to avoid the need for schlicht-function assumptions. Two examples of cubically convergent methods are given one of which is Halley's method.
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zero finding
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higher order convergence
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iterative methods
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analytic functions
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schlicht-function
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Halley's method
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