A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions (Q2465897)
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| Language | Label | Description | Also known as |
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| English | A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions |
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A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions (English)
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10 January 2008
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The nonlinear equation \(f(x) = 0\), where \(f\) is Fréchet differentiable in a convex subset of a Banach space, is approximated by Newton-like methods. The author proves conditions sufficient for its convergence. These conditions rely upon a generalized Lipschitz-type condition on the derivative of \(f\).
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nonlinear operator equation
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Banach space
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Newton-like method
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convergence
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