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A new convergence theorem for Steffensen’s method on Banach spaces and applications. (English) Zbl 0895.65024

The author proves a semilocal convergence theorem for Steffensen’s method, applied for approximating a locally unique solution of the equation \(f(x)=0\), where \(f\) is a twice FrĂ©chet-differentiable continuous operator on a closed convex domain \(D\) of a Banach space with values in a Banach space. As shown by an example, the convergence region thus obtained is larger than the ones given in other related papers.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
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