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An interesting example is given by:
Coeff_App(1)= INTERVAL(-3.1,-2.9);Coeff_App(2)=INTERVAL(1.9,2.1);
which leads to Lower=[1.1487,1.42957], Upper=[1.15224,1.43049].

The above procedure may give some sharp bounds. For example consider the Wilkinson polynomial of order 22 (which has as roots 1,2,$\ldots$,21,22) we get 0 negative roots while the positive roots are bounded by [0.790447,22.1087].

The test program Test_Bound_UP enable to test the bound procedures for any polynomial. This program take as first argument the name of a file giving the coefficients of the polynomial by increasing power of the variable. The program will print the bounds determined by all the previous procedures and then the bounds determined using the global implementation. Then the same treatment will be applied on the interval polynomial whose coefficients are intervals centered at the coefficients find in the file with a width of 0.2

Jean-Pierre Merlet 2012-12-20