High order iterative methods for approximating square roots (Q1914878)
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scientific article; zbMATH DE number 885561
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | High order iterative methods for approximating square roots |
scientific article; zbMATH DE number 885561 |
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High order iterative methods for approximating square roots (English)
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17 September 1997
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The authors describe an iteration function \(g_m(x)\) with \(m\geq 2\) having the propriety that for any initial iterate \(x_0> \sqrt \alpha\), the sequence of fixed-point iteration \(x_{k+1} =g_m (x_k)\) converges monotonically to \(\sqrt \alpha\) having \(m\)-th order rate of convergence. This function generalizes Newton's and Halley's iteration functions.
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square roots
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iteration function
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fixed-point iteration
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convergence
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Newton's and Halley's iteration functions
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