
Section 9.2 Differentiation arithmetic, enclosures of derivatives 321
x
f.x/
Figure 9.4. Global optimization.
for the global minimum can be computed faster than an approximation delivered by
conventional techniques whose quality is still uncertain.
These methods, of course, can also be used for a fast and highly accurate computa-
tion of the range of values of a function in a given domain.
9.2 Differentiation arithmetic, enclosures of derivatives
For many applications in scientific computing the value of the derivative of a function
is needed. The interval Newton method requires the computation of an enclosure of
the first derivative of the function ove ...