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A unifying theorem on Newton’s method in a Banach space with a convergence structure under weak assumptions. (English) Zbl 1029.65058
The author provides a semilocal convergence analysis for Newton’s method on a Banach space with a convergence structure. The obtained main result contains as special cases earlier results on semilocal convergence theorems of Newton-Kantorovich-type as well as global results on monotonicity. It turns out that under the same hypotheses the author’s sufficient convergence conditions are weaker and the error bounds on the distances involved finer than before. Some numerical examples support the theoretical results.
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
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