Extending the applicability of Newton’s method using Wang’s– Smale’s αα–theory

Ioannis K. Argyros, Santhosh George

We improve semilocal convergence results for Newton’s method by defining a more precise domain where the Newton iterate lies than in earlier studies using the Smale’s αα— theory. These improvements are obtained under the same computational cost. Numerical examples are also presented in this study to show that the earlier results cannot apply but the new results can apply to solve equations.

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George, Santhosh, Argyros, Ioannis, K.