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Accessibility of solutions by Newton’s method. (English) Zbl 0844.47035

Summary: We give new conditions for the convergence of Newton’s method in Banach spaces, in terms of the degree of logarithmic convexity. These conditions guarantee the convergence of Newton sequence in cases where the hypothesis of the Kantorovich theorem are not verified, as we show in some examples.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
65J15 Numerical solutions to equations with nonlinear operators
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[1] DOI: 10.1137/0711002 · Zbl 0284.65042 · doi:10.1137/0711002
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