Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative
Keywords:Halley's method, Fréchet-derivative, Banach space, semi-local convergence, Frechet derivative, centered Lipschitz condition
AbstractWe present a semi-local as well as a local convergence analysis of Halley's method for approximating a locally unique solution of a nonlinear equation in a Banach space setting.
We assume that the second Fréchet-derivative satisfies a centered Lipschitz condition.
Numerical examples are used to show that the new convergence criteria are satisfied but earlier ones are not satisfied.
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