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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.

MSC:
65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
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