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Next: 3.4.5 Charts Up: 3.4 Polynomial Interval Arithmetic Previous: 3.4.3 Optimality

3.4.4 Piecewise Models

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.


next up previous notation contents
Next: 3.4.5 Charts Up: 3.4 Polynomial Interval Arithmetic Previous: 3.4.3 Optimality
Jeff TupperMarch 1996