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###

Example 4

In this example (see section 15.1.3) we deal with a complex problem
of three equations in three unknowns
.
We are looking for a solution in the domain:

The system has a solution which is approximately:

This problem is extremely ill conditioned as for the `TestDomain`
the functions intervals are:

This program is implemented under the name `Test_Solve_General`.
With `espsilonf`=0 and `epsilon`=0.001 and if we stop at the
first solution we find with the maximum equation ordering:

with 531 boxes. We may also mention the following
remarks:
- we get no improvement with
the single bisection mode as we need 2435 boxes to find the
first solution,
- using the Reverse Storage mode does not lead to any improvement
for finding the first root: in this mode we need 5587 boxes
to get the first solution,

With the maximum middle-point equation ordering we find:

with 203 boxes.
The importance of normalizing the functions appears if we use `epsilonf`=0.1 and `epsilon`=0. If we stop at the first solution we
find:

while if we divide the first function by 1000 we find:

in four time less computation time.

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** Previous:** Example 3
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Jean-Pierre Merlet
2012-12-20