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,].
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