چکیده (انگلیسی):

We consider a modi$cation of the Newton method for $nding a zero of a univariate function. The case of multiple roots is not treated. It is proven that the modi$cation converges cubically. Per iteration it requires one evaluation of the function and two evaluations of its derivative. Thus, the modi$cation is suitable if the calculation of the derivative has a similar or lower cost than that of the function itself. Classes of such functions are sketched and a numerical example is given.