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Convergence of Newton’s method and inverse function theorem in Banach space. (English) Zbl 0923.65028
The author studies the convergence of the Newton’s method under some Lipschitz-type conditions and gives exact estimates for the radius of the ball in the inverse function theorem. The best possible a priori and a posteriori error bounds are also obtained. Improvements of convergence theorems under Kantorovich and respectively Smale type assumptions are obtained as particular cases of the main results in this paper.

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
Full Text: DOI
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