Local convergence of Newton-like methods for generalized equations (Q2479220)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local convergence of Newton-like methods for generalized equations |
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Local convergence of Newton-like methods for generalized equations (English)
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26 March 2008
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The local convergence analysis of the Newton-like method \[ 0\in f(x_k)+g(x_k)(\nabla f(x_k)+[x_{k-1},x_k;g])(x_{k+1}-x_k)+F(x_{k+1}); k\geq 0 \] towards a solution \(x^*\) of \(0\in f(x)+g(x)+F(x)\) is discussed; precisely, this process is super-linear under mild hypotheses. This conclusion is also true for its associated regula-falsi and the secant-type methods.
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Banach space
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multivalued nonlinear operator equation
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Newton-like method
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Fréchet differential
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divided difference
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pseudo-Lipschitz condition
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regula-falsi method
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set-valued map
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local convergence
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radius of convergence
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