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A modified Newton method for root finding with cubic convergence

Homeier, H. H. H.


Abstract We consider a modification of the Newton method for finding a zero of a univariate function. The case of multiple roots is not treated. It is proven that the modification converges cubically. Per iteration it requires one evaluation of the function and two evaluations of its derivative. Thus, the modification is suitable if the calculation of the derivative has a similar or lower cost ...


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