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

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 tex2html_wrap_inline34165 into sections where each section attains the extreme values of g:  

math19323

math13835

where

math19338

When evaluating tex2html_wrap_inline35733 , we may simply return tex2html_wrap_inline34911 if any of the aforementioned sections lie within m:

math19348

As with the previous sectioning scheme, there will often be a preferred sectioning, denoted by tex2html_wrap_inline36275 , which we will use to check containment.

The preferred sectioning tex2html_wrap_inline36277 of the sine function includes members from the preferred sectioning tex2html_wrap_inline36279 of the sine function:

math19357

math19363

In general, all members of tex2html_wrap_inline34915 may be transferred into tex2html_wrap_inline36275 , since tex2html_wrap_inline36285 may be defined without reference to the underlying interval number system. We may add another set of intervals to tex2html_wrap_inline36287 :

math19370

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


next up previous notation contents
Next: 3.3.16 Partial Functions Up: 3.3 Linear Interval Arithmetic Previous: 3.3.14 Example with a Piecewise
Jeff TupperMarch 1996