Next: 3.2.13 Examples with Monotonic Functions
Up: 3.2 Constant Interval Arithmetic
Previous: 3.2.11 Monotonically Decreasing Functions
We have concentrated on upper bounds since lower bounds may be
easily constructed using the rules given for upper bounds.
This is achieved with the following identity:
which follows directly from the definition of extremal bounds.
Given that 
is an upper bound of 
,
it follows that 
is a lower
bound of 
:
The proof is valid for all 
since it only relies on properties of 
.
So both lower and upper bounds for 
may be constructed
from the upper bounds of 
and :
A similar process allows construction with lower bounds:
We do assume that the number system underlying the interval number system
has an exact negation operator which is total. Although the above construction
could be taken literally, it is mainly a device to simplify exposition.
In practice, upper and lower bounds are usually computed simultaneously
by a single procedure.
Next: 3.2.13 Examples with Monotonic Functions
Up: 3.2 Constant Interval Arithmetic
Previous: 3.2.11 Monotonically Decreasing Functions
