On the construction of iterative methods with at least cubic convergence. (English) Zbl 1122.65326

Summary: Using the iteration formulas of order two for solving nonlinear equations, we present a basic tool for deriving new higher order iterative methods that do not require the computation of the second-order or higher-order derivatives. The presented convergence analysis shows that the order of convergence of the obtained iterative methods are three or higher. The comparison with other methods is given.


65H05 Numerical computation of solutions to single equations
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