Coeff_App(1)= INTERVAL(-3.1,-2.9);Coeff_App(2)=INTERVAL(1.9,2.1); Coeff_App(3)=INTERVAL(-1.1,-0.9);Coeff_App(4)=INTERVAL(0.9,1.1); Num=Global_Positive_Bound_Interval(3,Coeff_App,Lower,Upper);which leads to

The above procedure may give some sharp bounds. For example consider the Wilkinson polynomial of order 22 (which has as roots 1,2,,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