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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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