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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 tex2html_wrap_inline31401 , given tex2html_wrap_inline32577 . We now consider implementing tex2html_wrap_inline36293 . As before,

math13897

The function tex2html_wrap_inline36295 ,  

math19385

when given an interval m and a set tex2html_wrap_inline31241 of extended real numbers, produces a valid description of the relationship between m and tex2html_wrap_inline31241 , in terms of the provided set tex2html_wrap_inline36305 , of extended real numbers:

math19391

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

math19395

The function tex2html_wrap_inline36295 ``translates'' from tex2html_wrap_inline31241 to tex2html_wrap_inline36305 .

For the function tex2html_wrap_inline34165 , an evaluation of the model tex2html_wrap_inline36293 proceeds as follows:

math19402

The evaluation of tex2html_wrap_inline36293 is analogous to the evaluation of tex2html_wrap_inline34927 .

The resulting domain description f'(d'); tex2html_wrap_inline36323 , tex2html_wrap_inline36325 ; is determined using f(d), tex2html_wrap_inline31241 , tex2html_wrap_inline36305 , and tex2html_wrap_inline36295 :

math19413

The set tex2html_wrap_inline31241 , given by tex2html_wrap_inline34931 , corresponds to tex2html_wrap_inline36339 :

math19417

The set tex2html_wrap_inline36305 , given indirectly by tex2html_wrap_inline36343 , similarly corresponds to tex2html_wrap_inline33295 :  

math19423

the function tex2html_wrap_inline36347 is chosen, by tex2html_wrap_inline36349 , to facilitate the impending computation of tex2html_wrap_inline36351 . The chosen tex2html_wrap_inline36347 is used to describe the domain of tex2html_wrap_inline36355 .

The resulting value v', tex2html_wrap_inline36359 , depends on f'(d'). If tex2html_wrap_inline36363 , the resulting value is given by the methods outlined earlier:

math19431

If tex2html_wrap_inline36365 , the resulting value is arbitrary:

math19436


next up previous notation contents
Next: 3.3.17 Examples with a Partial Up: 3.3 Linear Interval Arithmetic Previous: 3.3.15 Periodic Functions
Jeff TupperMarch 1996