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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.
Next: 3.3.16 Partial Functions
Up: 3.3 Linear Interval Arithmetic
Previous: 3.3.14 Example with a Piecewise