  In this article, we discuss sixth-order and seventh-order iterative methods
for nonlinear equations. Derivative-based and derivative-free, both categories
are presented for said iterative methods. Especially sixth-order
derivative-based and derivative-free iterative families are constructed in such
a way that they circumstance a wide class of sixth-order methods which are
developed in last many years. Weight functions are introduced to enhance the
efficiency and parametric combination gives weight-age flexibility in between
weight functions.
