We tested our computed integration formulae on six different functions described in Table 1.

j | ||

1 | ||

2 | ||

3 | ||

4 | ||

5 | ||

6 | 0 |

Table

Figure 7 and 8 show these integration errors for all computed formulae and all test functions. A detailed list of integration errors is contained in Tables 6 and 7 (see appendix). Since the machine precision is about , the computed formulae have a "treshold" at about . Without a doubt, the errors will get smaller when the numerical integration is done on a machine with higher machine precision (or which simulates more accurate floating point numbers by software).

Unfortunately, to the best of our knowledge, comparable numerical results for integration formulae do not seem to be available in the literature.

Thu Dec 23 19:39:35 CET 1999