On a class of Newton-type methods (Q1094103)
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scientific article; zbMATH DE number 4024651
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a class of Newton-type methods |
scientific article; zbMATH DE number 4024651 |
Statements
On a class of Newton-type methods (English)
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1987
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The author investigates the following modification of the Kantorovich method \(x_{n+1}=x_ n-[P'((x_ n+\Omega (x_ n))/2)^{-1}]P(x_ n),\) \(n=0,1,...\), for the equation \(P(x)=0\). \(\Omega\) (x) is an operator that generates an iteration formula of order \(\tau\), \(1\leq \tau \leq 2\), and P(x) is a nonlinear operator from one Banach space to another Banach space.
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Newton-type methods
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Kantorovich method
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iteration formula
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Banach space
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