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Semilocal Convergence Theorem for a Newton-like Method
Published online by Cambridge University Press: 07 September 2017
Abstract
The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.
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- Copyright © Global-Science Press 2017