A convergence improvement factor and higher-order methods for solving nonlinear equations (Q419546)
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scientific article; zbMATH DE number 6036580
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A convergence improvement factor and higher-order methods for solving nonlinear equations |
scientific article; zbMATH DE number 6036580 |
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A convergence improvement factor and higher-order methods for solving nonlinear equations (English)
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18 May 2012
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convergence improvement factor
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nonlinear equations
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higher-order methods
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iterative scheme
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The following iterative scheme for the equation \(f(x) = 0\) is studied: NEWLINE\[NEWLINE z_n = \phi _p (x_n ),\quad x_{n + 1} = z_n - h(\mu _n )\frac{f(z_n )}{{f}'(x_n )}, NEWLINE\]NEWLINE where \(\mu _n = \frac{f(y_n )}{f(x_n )}\), \(y_n = x_n - \frac{f(x_n )}{{f}'(x_n )}\), \(\phi _p ( \cdot )\) is an arbitrary iteration with convergence order \(p,\) and \(h( \cdot )\) is a sufficiently smooth function.
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