3.3.15 Periodic Functions

 

As with constant interval arithmetic, special care should be taken when evaluating periodic functions to avoid unnecessary computation.

We will again cut the function into sections where each section attains the extreme values of g:  

where

When evaluating , we may simply return if any of the aforementioned sections lie within m:

As with the previous sectioning scheme, there will often be a preferred sectioning, denoted by , which we will use to check containment.

The preferred sectioning of the sine function includes members from the preferred sectioning of the sine function:

In general, all members of may be transferred into , since may be defined without reference to the underlying interval number system. We may add another set of intervals to :

This set is intrinsic to linear interval arithmetic: it need not transfer to another polynomial interval arithmetic.

Jeff Tupper

March 1996