Two weighted eight-order classes of iterative root-finding methods

In this paper we design, by using the weight function technique, two families of iterative schemes with order of convergence eight. These weight functions depend on one, two and three variables and they are used in the second and third step of the iterative expression. Dynamics on polynomial and non-polynomial functions is analysed and they are applied on the problem of preliminary orbit determination by using a modified Gauss method. Finally, some standard test functions are to check the reliability of the proposed schemes and allow us to compare them with other known methods.