  To approximate a simple root of an equation we construct families of
iterative maps of higher order of convergence. These maps are based on model
functions which can be written as an inner product. The main family of maps
discussed is defined recursively and is called {\it Newton-barycentric}. We
illustrate the application of Newton-barycentric maps in two worked examples,
one dealing with a typical least squares problem and the other showing how to
locate simultaneously a great number of extrema of the Ackley's function.
