A modification of Cauchy's method for quadratic equations (Q2465856)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A modification of Cauchy's method for quadratic equations |
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A modification of Cauchy's method for quadratic equations (English)
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10 January 2008
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The locally unique solution to a nonlinear equation \(F(x)=0\), where \(F\) is a quadratic mapping on an open convex subset of a Banach space, is approximated by a modified Cauchy method. The author studies the \(R\)-order of convergence assuming that \(F\) is twice Fréchet differentiable. The results are applied to an integral equation of Hammerstein type and complex as well as real quadratic equations.
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quadratic operator equation in a Banach space
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Hammerstein integral equation
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Cauchy's method
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semilocal convergence
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apriori error estimates
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\(R\)-order of convergence
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Banach space
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