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On the convergence of Newton’s method for analytic operators. (English) Zbl 1029.65057
The author studies the problem of approximating a solution of an equation $$F(x)=0$$ using Newton’s method, where $$F$$ is an analytic operator defined on an open convex subset of a Banach space $$X$$ with values in a Banach space $$Y$$. New local and semilocal convergence theorems are presented. These results are completed with a numerical example.
##### MSC:
 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators
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