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Weaker conditions for the convergence of Newton’s method. (English) Zbl 1245.65058
The authors present new criteria for the convergence of Newton’s method in finding an approximate solution of a nonlinear operator equation in a Banach space setting. The first result uses the center-Lipschitz condition. The second result uses Lipschitz and center-Lipschitz conditions on the Fréchet derivative of the involved operator. Some numerical examples are provided for which the weaker convergence criteria are satisifed.

MSC:
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
Software:
NewtonLib
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