Hansen-Ptrick's family is of Laguerre's type


Ljiljana D. Petković, Miodrag S. Petković, Dragan Živković




We studied a class of cubically convergent iterative methods for simple and multiple zeros of analytic functions and to investigate their mutual dependence and showed that one-parameter Hansen-Patrick’s family (1977) is not a new one but it simply follows directly from the classical Laguerre method. In addition, new derivations of Laguerre’s method for simple and multiple zeros are given and some special cases are presented.