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Example 3

This example is derived from example 2. We notice that in the three functions of example 2 the second degree terms of $x,y$ are for all functions $x^2+y^2$. Thus by subtracting the first function to the second and third we get a linear system in $x,y$. This system is solved and the value of $x,y$ are substituted in the first function. We get thus a system of one equation in the unknown $\theta$ (see section 15.1.2). The roots of this equation are 0,-0.806783438. The test program is Test_Solve_General2. The IntervalFunction is written as:
INTERVAL_VECTOR IntervalTestFunction (int l1,int l2,INTERVAL_VECTOR & in)
return xx;
This program is implemented under the name Test_Solve_General2. With epsilonf=0 and epsilon=0.001 we get the solution intervals, using 32 boxes:


for whatever order. If we use epsilon=0 and epsilonf=0.1 we get, using 50 boxes:

&& \theta=[-0.806784012741056,-0.806781016684830]\\
&& \theta=[-4.793689962142628e-05,0]

In both cases the solution intervals contain the roots of the equation.

Jean-Pierre Merlet 2012-12-20