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• W2091221376 abstract "We provide sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear operator equation containing operators that are Fréchet-differentiable of order at least two, in a Banach space setting. Numerical examples are also provided to show that our results apply to solve nonlinear equations in cases earlier ones cannot [J.M. Gutiérrez, A new semilocal convergence theorem for Newton’s method, J. Comput. Appl. Math. 79(1997) 131–145; Z. Huang, A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993) 211–217; F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Mathematica 5 (1985) 71–84]." @default.
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• W2091221376 date "2009-10-01" @default.
• W2091221376 modified "2023-09-26" @default.
• W2091221376 title "On Newton’s method for solving equations containing Fréchet-differentiable operators of order at least two" @default.
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• W2091221376 doi "https://doi.org/10.1016/j.amc.2009.07.005" @default.
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