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Convergence behavior for Newton-Steffensen’s method under Lipschitz condition of second derivative. (English) Zbl 1270.65026
The paper under review deals with the local and semilocal convergence problems for the Newton-Steffensen method applied to nonlinear operator equations in Banach spaces. Under the hypothesis that the second derivative of the operator considered satisfies the Lipschitz condition, the authors obtain a convergence criterion for the Newton-Steffensen method.
MSC:
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J05 Equations involving nonlinear operators (general)
65H10 Numerical computation of solutions to systems of equations
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