Next: 3.3.17 Examples with a Partial Up: 3.3 Linear Interval Arithmetic Previous: 3.3.15 Periodic Functions

## 3.3.16 Partial Functions

We have considered implementing a model , given . We now consider implementing . As before,

The function ,

when given an interval m and a set of extended real numbers, produces a valid description of the relationship between m and , in terms of the provided set , of extended real numbers:

The relationship between each interval and its associated set is that of containment, defined as before:

The function ``translates'' from to .

For the function , an evaluation of the model proceeds as follows:

The evaluation of is analogous to the evaluation of .

The resulting domain description f'(d'); , ; is determined using f(d), , , and :

The set , given by , corresponds to :

The set , given indirectly by , similarly corresponds to :

the function is chosen, by , to facilitate the impending computation of . The chosen is used to describe the domain of .

The resulting value v', , depends on f'(d'). If , the resulting value is given by the methods outlined earlier:

If , the resulting value is arbitrary:

Next: 3.3.17 Examples with a Partial Up: 3.3 Linear Interval Arithmetic Previous: 3.3.15 Periodic Functions
 Jeff Tupper March 1996