Author： Argyros Ioannis
Publisher： Taylor & Francis Ltd
ISSN： 0020-7160
Source： International Journal of Computer Mathematics, Vol.84, Iss.12, 2007-12, pp. : 1747-1756
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Abstract
In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in Banach space using Newton's method. The differentiability of the operator involved is not assumed, and we use Hölderian assumptions. We provide a semilocal convergence analysis based on a suitable point-based approximation. Our approach is justified by numerical examples where our results apply, whereas earlier ones cannot be applied in this way.
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