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The improvements of modified Newton’s method. (English) Zbl 1122.65332
Summary: We improve some third-order modifications of Newton’s method and obtain many new methods for solving non-linear equations. The new methods have the order of convergence five or six. Per iteration these methods require two evaluations of the function and two evaluations of its first derivative and therefore the efficiency of the new methods may also be improved. These methods can compete with Newton’s method, as we show in some examples.

MSC:
65H05Single nonlinear equations (numerical methods)