Once we have in terms of constructing a p-th order iteration is a simple matter. We illustrate the construction for p=2. We take as our initial value. We could have used any value from Table 2. We define two sequences and :Here we consider as a function of r. From (3.19) and (3.20) we have From (3.18) and (4.6) we have for Equations (4.9)--(4.12) uniquely define the two sequences and . The convergence is quadratic. We illustrate with a MAPLE session. > read iteration1: > it1(5,100); The function it1(5,100) computes the first 5 iterations to 100 digits and an approximation for the difference between and . We also note that this iteration is really a known quadratic iteration [6, Iteration 3.6, p. 700,].