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Next: 3.3.27 Partial Binary Functions Up: 3.3 Linear Interval Arithmetic Previous: 3.3.25 Binary Functions: One-Step Method

3.3.26 Examples with a Binary Function

Consider the division function, tex2html_wrap_inline35491 ,

math16326

math16336

The evaluation of tex2html_wrap_inline37155 ,

math23380

proceeds as follows:

math23388

The sign of tex2html_wrap_inline37203 and tex2html_wrap_inline37205 are determined by the arguments and the relationship with the second derivative of tex2html_wrap_inline37207 :

math23424

math23433

The corresponding evaluation with constant intervals produces a noticeably larger result:

math23442

Similar behaviour may be observed near the origin with the general exponentiation function, tex2html_wrap_inline35139 .


next up previous notation contents
Next: 3.3.27 Partial Binary Functions Up: 3.3 Linear Interval Arithmetic Previous: 3.3.25 Binary Functions: One-Step Method
Jeff TupperMarch 1996