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Semilocal convergence for Halley’s method under weak Lipschitz condition. (English) Zbl 1187.65059

Let X,Y be Banach spaces, D be an open convex part of X and F:DY be a continuous, twice Fréchet differentiable operator. The semilocal convergence of the Halley’s method

x k+1 =x k -(I-L F (x k )) -1 F ' (x k ) -1 F(x k ),k0,

towards the unique solution x * of F(u)=0 is established, under Lipschitz type assumptions involving the second derivative of F.

65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
65R20Integral equations (numerical methods)
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