A new semilocal convergence theorem for Newton's method |
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Institution: | University of La Rioja, Dpt. Mathematics and Computation, C/Luis de Ulloa s/n, 26004, Logroño, Spain |
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Abstract: | A new semilocal convergence theorem for Newton's method is established for solving a nonlinear equation F(x) = 0, defined in Banach spaces. It is assumed that the operator F is twice Fréchet differentiable, and F″ satisfies a Lipschitz type condition. Results on uniqueness of solution and error estimates are also given. Finally, these results are compared with those that use Kantorovich conditions. |
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