In this paper, we design two parametric classes of iterative methods
without memory to solve nonlinear systems, whose convergence order is
four and seven, respectively. From their error equations and to increase
the convergence order without performing new functional evaluations,
memory is introduced in these families of different forms. That allows
us to increase from four to seven the convergence order in the first
family and from seven to eleven in the second one. We perform some
numerical experiments with big size systems for confirming the
theoretical results and comparing the proposed methods along other known
schemes.