Note on derivative-free iteration method with global convergence (Q2765639)
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scientific article; zbMATH DE number 1694927
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on derivative-free iteration method with global convergence |
scientific article; zbMATH DE number 1694927 |
Statements
6 December 2002
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null point
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continuous function
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derivative-free iteration method
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global convergence
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Note on derivative-free iteration method with global convergence (English)
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To calculate a null point of a continuous function \(f(x)\) in an interval \([a, b]\) with \(f(a)\cdot f(b)<0\), the authors consider the iterative method \(x_{n+1}=x_n-h_nf(x_n), ~n=0,1,2 \ldots\). Here \(x_0=b\) or \(a\) and \(f(x)\) has a unique null point in \([a,b]\). Convergence of the method and techniques of how to choose the stepsize \(h_n\) are discussed.
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