As before, we may construct general polynomial interval operators by considering subdomains of the function to be implemented. As discussed earlier, optimal bounds are known when the n+1st derivative is bounded away from zero. When an interval straddles a zero of the n+1st derivative, the n+kth derivative will often be bounded away from zero. In such a case, an n+k-1 degree polynomial may be used to bound the function, which may then be demoted to find an n degree polynomial bound.
| Jeff Tupper | March 1996 |