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A local convergence analysis and applications of Newton’s method under weak assumptions. (English) Zbl 1029.65056

A local convergence theorem for Newton’s method in a Banach space is provided. The author uses Lipschitz as well as center Lipschitz conditions and small majorizing sequences to obtain more precise error bounds and a larger convergence radius than before. This study is completed with a numerical example.

MSC:

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