REMARKS ON THE CONVERGENCE OF NEWTON'S METHOD UNDER HÖLDER CONTINUITY CONDITIONS
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Abstract
We use a Newton-like iteration to solve the nonlinear op erator equation in a Banach space. The basic assumption is that the Fréchet-derivative of the nonlinear operator is Hölder continuous on some open ball centered at the initial guess. Under natural assumptions, we prove linear convergence of the iteration to a locally unique solution of the nonlinear equation.
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