Contents
** Next:** The Quadratic and
**Up:** The Symbolic Search
** Previous:** Modular Equations

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,].

Contents
** Next:** The Quadratic and
**Up:** The Symbolic Search
** Previous:** Modular Equations